Hi I'm Aleck, ask me anything...

About me: I’m Smart Aleck, your trusty Answer Bot. I use AI to answer your questions simply and clearly. Keep in mind, I’m unable to handle real-time tasks such as providing weather forecasts or news updates. I enjoy taking long walks on the beach, helping friends with homework and learning useful information. Ask away!

Solve the differential equation dy/dx +8y = 4 when y(0) = 2

Answer

The solution to the equation dy/dx + 8y = 4 when y(0) = 2 is y = 2 e^8x.

Explanation

The differential equation dy/dx + 8y = 4 is a first-order linear differential equation with constant coefficients. It can be solved using the integrating factor method. The integrating factor is e^8x, and when this integrating factor is multiplied with the given equation, the equation becomes e^8x(dy/dx + 8y) = 4e^8x . Integrating both sides of the equation gives us e^8xy = 4/8∫e^8xdx + c, where c is the constant of integration.

Solution

Since we are given the initial condition y(0) = 2, we can use this to calculate the value of c. Substituting x = 0 and y = 2 in e^8xy = 4/8∫e^8xdx + c, we get 2 = c. Thus, the solution is y = 2 e^8x.

Examples

If x = 3, then y = 2 e²⁴
If x = -2, then y = 2 e^-16
If x = 0.5, then y = 2 e⁴

Related Questions

What is the general solution to the differential equation dy/dx + 8y = 4?
How do you solve a first order linear differential equation?
What is the integrating factor method?
What is the solution to the equation dy/dx + y = 4 when y(0) = 5?
How do you solve a differential equation with initial conditions?
What is the solution to the equation dy/dx + 3y = 5 when y(0) = -2?
What is the solution to the equation dy/dx – 4y = 8 when y(0) = 6?
How do you solve a non-homogeneous differential equation?
What is the integrating factor of the differential equation dy/dx + 4y = 6?
What is the solution to the equation dy/dx + xy = x when y(0) = 1?

Recent Questions

Critically discuss the various factors that influence consumer behaviour in the fashion retail industry and provide examples to support your answer.

Other Creditors-Withholding Taxes

Question 4 (20 Marks) Consider the scenario in question three above. As part of the marketing, what decisions would you pay attention to as you design the channels to distribute your new product? What channels should be used to distribute the new product?

What channels should be used to distribute the new product?

Different types of climate zones

Input Tax – Deferred Tax

Suppose 20 households in a community have the demand function Q = 2 – 0.001P each for streetlights while 5 other households have the demand function Q = 3 – 0.002P each for streetlights. Here, Q refers to the number of streetlights to erect near their home while P is the unit price of each streetlight. The cost of building each streetlight is GHS 45. a) Assuming each household is making its separate purchase decision, find the market demand function for streetlights for all 25 households b) Assuming each household is making its separate purchase decision, find the equilibrium price and number of streetlights in the community c) Assuming a community association has decided to coordinate this streetlight purchase decision problem. The community leader uses the demand functions to determine how much each household is willing to contribute (willingness to pay) towards the first, second, third, etc streetlight. The first light is purchased only when the sum of individual households’ contributions is at least equal to the marginal cost of streetlights. Find out how many streetlights are purchased for this community in equilibrium.

Suppose 20 households in a community have the demand function Q = 2 – 0.001P each for streetlights while 5 other households have the demand function Q = 3 – 0.002P each for streetlights. Here, Q refers to the number of streetlights to erect near their home while P is the unit price of each streetlight. The cost of building each streetlight is GHS 45. a) Assuming each household is making its separate purchase decision, find the market demand function for streetlights for all 25 households b) Assuming each household is making its separate purchase decision, find the equilibrium price and number of streetlights in the community c) Assuming a community association has decided to coordinate this streetlight purchase decision problem. The community leader uses the demand functions to determine how much each household is willing to contribute (willingness to pay) towards the first, second, third, etc streetlight. The first light is purchased only when the sum of individual households’ contributions is at least equal to the marginal cost of streetlights. Find out how many streetlights are purchased for this community in equilibrium. Explain your answers in details

Suppose 20 households in a community have the demand function Q = 2 – 0.001P each for streetlights while 5 other households have the demand function Q = 3 – 0.002P each for streetlights. Here, Q refers to the number of streetlights to erect near their home while P is the unit price of each streetlight. The cost of building each streetlight is GHS 45. a) Assuming each household is making its separate purchase decision, find the market demand function for streetlights for all 25 households b) Assuming each household is making its separate purchase decision, find the equilibrium price and number of streetlights in the community c) Assuming a community association has decided to coordinate this streetlight purchase decision problem. The community leader uses the demand functions to determine how much each household is willing to contribute (willingness to pay) towards the first, second, third, etc streetlight. The first light is purchased only when the sum of individual households’ contributions is at least equal to the marginal cost of streetlights. Find out how many streetlights are purchased for this community in equilibrium.

The daily demand function for a product is given by Q=1,010−2P , where Q stands for the quantity demanded, and P stands for the price.

Suppose 20 households in a community have the demand function Q = 2 – 0.001P each for streetlights while 5 other households have the demand function Q = 3 – 0.002P each for streetlights. Here, Q refers to the number of streetlights to erect near their home while P is the unit price of each streetlight. The cost of building each streetlight is GHS 45. a) Assuming each household is making its separate purchase decision, find the market demand function for streetlights for all 25 households b) Assuming each household is making its separate purchase decision, find the equilibrium price and number of streetlights in the community c) Assuming a community association has decided to coordinate this streetlight purchase decision problem. The community leader uses the demand functions to determine how much each household is willing to contribute (willingness to pay) towards the first, second, third, etc streetlight. The first light is purchased only when the sum of individual households’ contributions is at least equal to the marginal cost of streetlights. Find out how many streetlights are purchased for this community in equilibrium.

Suppose households attempt to save more, so that consumer confidence falls. In an IS–LM diagram where the central bank moves interest rates to keep output constant, show the effect of the fall in consumer confidence on the equilibrium in the economy

Here, we consider the effect of a drop in consumer confidence on private saving and investment in the context of the IS–LM framework, in which investment depends on the interest rate and output but the central bank moves interest rates to keep output constantt. a) Suppose households attempt to save more, so that consumer confidence falls. In an IS–LM diagram where the central bank moves interest rates to keep output constant, show the effect of the fall in consumer confidence on the equilibrium in the economy. b) How will the fall in consumer confidence affect consumption, investment and private saving? Will the attempt to save more necessarily lead to more saving? Will this attempt necessarily lead to less saving

what are the key researcher who worked on the relationship between crop diversification as a rainfed farming system management strategy and climate change and socio-economic determinants of adaptation

how the culture of consumption started?

An economy is currently in a recession caused by a shift in aggregate demand, given time, the economy can adjust itself back to potential output (in the long run) as the expected price level a. rises, shifting aggregate demand curve to the right. b. rises, shifting aggregate demand curve to the left. c. falls, shifting aggregate demand curve to the right. d. falls, shifting short-run aggregate supply curve to the right. e. falls, shifting short run aggregate supply curve to the left.

Dead phone and pc logo

Identify the part of speech for the highlighted word in the sentence, which is fuzzy. My fuzzy blanket sat on the edge of my couch in my living room.

Identify the part of speech for the highlighted word in the sentence. My fuzzy blanket sat on the edge of my couch in my living room.

Read the sentence and determine the meaning of the word using context clues and your prior knowledge. Then, explain what clues in the sentence helped you determine the meaning. I wanted to just finish setting the table, but my mother scrupulously arranged each napkin, dish and utensil until they were in perfect alignment.

Which of the following sentences contains a comma splice? A) I went to the store, but I forgot to buy milk. B) Sarah loves to read books, and she enjoys writing stories. C) The cat climbed up the tree, it was afraid of the dog. D) John and Mary went to the park, and they played on the swings.

Read the following sentence and answer the question below. “The protagonist of the story embarked on a perilous adventure.” What does the word “protagonist” mean? A) A type of conflict in a story B) The main character in a story C) A sudden and unexpected event D) The setting of a story

What is the correct definition of the word “indignant”? A) Extremely happy B) Feeling or showing anger C) Full of energy and excitement D) Having a strong desire to succeed

Két tökéletesen versenyző vállalat, egy akkumulátorgyár és egy strand, egymástól nem messze működnek egy folyó partján. Az akkumulátorgyár költségfüggvénye TCA=5·A2+120·A. Az akkumulátorok ára 1120 Ft darabonként. A strand költségfüggvénye TCS=2·S2+10·S+80·A. A strandbelépő ára 410 Ft alkalmanként. Ekkor… 1 kérdésVálasszon ki egyet: a. a strand tevékenységének pozitív externális hatása van az akkumulátorgyár működésére. b. a strand tevékenységének negatív externális hatása van az akkumulátorgyár működésére. c. a strand tevékenységére negatív externális hatása van az akkumulátorgyár működésének. d. a strand tevékenységére pozitív externális hatása van az akkumulátorgyár működésén

Each of 1,000 identical firms in the competitive peanut butter industry has a short-run marginal cost curve given by SMC = 4 + Q. If the demand curve for this industry is P=10–2Q1000 , what will be the short-run loss in producer and consumer surplus if an outbreak of aflatoxin suddenly makes it impossible to produce any peanut butter? (Round your answers to the nearest whole number.) Producer Surplus: Numeric Response 1.Edit Unavailable. not attempted, incorrect. Consumer surplus: Numeric Response 2.Edit Unavailable. not attempted, incorrect. Explanation

Each of 1,000 identical firms in the competitive peanut butter industry has a short-run marginal cost curve given by SMC = 4 + Q. If the demand curve for this industry is P=10–2Q1000 , what will be the short-run loss in producer and consumer surplus if an outbreak of aflatoxin suddenly makes it impossible to produce any peanut butter? (Round your answers to the nearest whole number.) Producer Surplus: Numeric Response 1.Edit Unavailable. not attempted, incorrect. Consumer surplus: Numeric Response 2.Edit Unavailable. not attempted, incorrect. Explanation SR supply = ΣMCi MCi = 4 + Qi Qi = MCi − 4 = P − 4 ΣQi = Q = 1,000 − 4,000 Which means that industry supply is given by P = 4 + Q/1,000. SR equilibrium Q: 4 + Q/1,000 = 10 − 2Q/1,000 3Q/1,000 = 6, Q = 2,000, P = 6. Consumer surplus = area of upper triangle = (10 − 6) × 2,000/2 = 4,000 Producer surplus = area of lower triangle = (6 − 4) × 2,000/2 = 2,000 Total loss in surplus = 6,000

A) She likes to run, hiking, and biking. B) He wants to play basketball, jogging, and to swim. C) They can either go shopping or to watch a movie. D) I enjoy reading, writing, and solving puzzles.

Which of the following is an example of an informational text? A) A novel set in the future B) A poem about love and loss C) A newspaper article about climate change D) A fictional story about talking animals

Provide an example of: Direct tourism effect: Indirect tourism effect: Induced tourism effect:

Provide an example of: Tourism contribution: Tourism impact: Tourism benefit: with examples

Provide an example of: Tourism contribution: Tourism impact: Tourism benefit:

Suppose a destination which was visited by 20 000 tourists more in 2023. They spent on average $ 350 on their vacation. The regional GDP of the destination was $ 1.237 billion in 2022. The growth rate of the regional GDP was 1.3 %. What is the value of an output multiplier?

Suppose an economy for which mpc = 0.75 and an original French tourist’s expenditure in this economy was $ 250. Calculate first three steps of the multiplication: Further suppose that the marginal rate of income taxation is 0.2. How much will the GDP of the given destination’s country change in total?

Why measuring the economic benefits is so difficult?

Why mpc + mps is always equal to one?

What is the difference between direct, indirect, and induced effect? in economic par of view

What is the difference between direct, indirect, and induced effect?

What is the difference between direct and indirect contribution?

Suppose an economy for which mpc = 0.75 and an original French tourist’s expenditure in this economy was $ 250. Calculate first three steps of the multiplication:

what is the contribution of BPI in the Philippines capital market industry

fungsi permintaan bagi keluaran sebuah syarikat diberikan oleh P=60-Q. Kos tetap ialah 100, dan kos berubah bagi setiap barang ialah Q+6. Tuliskan ungkapan bagi jumlah kos, TC, dalam sebutan Q dan simpulkan bahawa fungsi purata diberikan oleh AC=Q+6+100/Q

Let market demand be given by the inverse demand curve P(Q) = 50−2Q, where Q = q1 + q2. The cost function for each of the two firms in the industry is C(qi) = 2qi . Firms are Cournot competitors. (a) Define the best-response function of a firm. Derive the best-response function of each firm. (b) Find for each firm in the Cournot equilibrium firm output and firm profits. What is the price that clears the market? Is the outcome efficient?

Carbon disulfide gas and oxygen gas react to form sulfur dioxide gas and carbon dioxide gas. What volume of sulfur dioxide would be produced by this reaction if 3.0m^3 of oxygen were consumed? Also, be sure your answer has a unit symbol, and is rounded to the correct number of significant digits.

Use the following graph of the market for cases of beer to answer the questions that follow. (Note: You will not be graded on any changes you make to the graph.) Scratch points 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0 Price of Beer (Dollars per case) Quantity of Beer (Thousands of cases) Demand Supply Complete the first row of the following table by entering the price paid by consumers, the price received by producers, and the quantity of beer sold in the absence of a tax on this market. Tax Price Paid by Consumers Price Received by Producers Quantity of Beer Sold (Dollars per case) (Dollars per case) (Dollars per case) (Thousands of cases) 0 4 Suppose the federal government requires beer drinkers to pay a $4 tax on each case of beer purchased. (In fact, both the federal and state governments impose beer taxes of some sort.) Complete the second row of the above table by entering the price paid by consumers, the price received by producers, and the quantity of beer sold when beer drinkers pay a $4 tax on each case of beer. As a result of the tax, the price producers receive . Continue without saving

Suppose the central bank in the nation of Zook attempts to pay off its national debt by printing large amounts of currency. The large increase in the money supply causes the price level to rise by 1,300 percent. What do you expect will happen to the value of Zook’s currency? Instructions: Round your answer to the nearest whole number. The value of Zook’s currency will decrease by percent.

the answer is incorrect i need juist the final answer

Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period. $21,000 quarterly paymetns for 13 years; interest rate 6.6% enter your response here. (Do not round until the final answer. Then round to the nearest cent as needed.) i need the final answer

Assume the value of a country’s currency is 1 when the price level is 0.75. Instructions: Enter your answers rounded to 2 decimal places. If you are entering any negative numbers be sure to include a negative sign (−) in front of those numbers. If the price level changes to 0.6, by how much in percentage terms will the value of the country’s currency change?

Assume that Jimmy Cash has $2,100 in his checking account at Folsom Bank and uses his checking account debit card to withdraw $210 of cash from the bank’s ATM machine. By what dollar amount did the M1 money supply change as a result of this single, isolated transaction? Instructions: Enter your answer as a whole number. $

At the equilibrium interest rate, what are the quantity of money supplied, the quantity of money demanded, the amount of money demanded for transactions, and the amount of money demanded as an asset in Trance? Quantity of money supplied = $ billion Quantity of money demanded = $ billion Amount of money demanded for transactions = $ billion Amount of money demanded as an asset = $ billion

Assume that the following data characterize the hypothetical economy of Trance: money supply = $200 billion; quantity of money demanded for transactions = $160 billion; quantity of money demanded as an asset = $10 billion at 12 percent interest, increasing by $10 billion for each 2-percentage-point fall in the interest rate. Instructions: Enter your answers as a whole number. What is the equilibrium interest rate in Trance? percent

final reflections on sociology

how to make a kel nuke omori

how to make a kel nuke

Monopolistic competition. Refer to the above graphs and answer the following questions… Group of answer choices Which graph represents a monopolistically competitive firm in long-run equilibrium? [ Choose ] In Figure 4, why is the ATC curve not tangent to the demand curve at its minimum? [ Choose ] Referring to Figure 1, how is the profit-maximizing production quantity determined? [ Choose ] For Figure 1, is this firm making a profit or a loss? [ Choose ] Which graph shows a firm incurring short-run losses [ Choose ] Referring to Figure 3, identify the lower right point of the profit or loss rectangle? [ Choose ] Referring to Figure 3, identify the upper right point of the profit or loss rectangle? [ Choose ] Referring to Figure 1, identify the upper right point of the profit or loss rectangle? [ Choose ] Referring to Figure 1, identify the lower right point of the profit or loss rectangle? [ Choose ] Referring to Figure 2, could this depict a monopolistically competitive firm incurring short-run losses?

Pouvez-vous expliquer comment la fonction de production CES intègre la notion d’élasticité constante de substitution ?

𝑞 = min (𝑧1^(𝛼) ,𝛽𝑧2 ) . Supposez que 𝛼 = 1. Est-il possible de donner l’expression de la fonction d’offre ? Justifiez votre réponse

𝑞 = min (𝑧1^(𝛼) ,𝛽𝑧2 ) . . Supposez que l’entreprise vend l’output à un prix 𝑝 fixe, trouvez les valeurs des paramètres 𝛼 et 𝛽 qui vérifient les conditions de second ordre pour la maximisation du profit.

𝑞 = min (𝑧1^(𝛼) ,𝛽𝑧2 ) . what is demand function for inputs

𝑞 = min (𝑧1^(𝛼) ,𝛽𝑧2 ) . what is demand function for imputs