Solve the differential equation, 5 (dy/dt) + 4y = 2, y(0) = 1 using Laplace transforms.

Answer

The differential equation 5 (dy/dt) + 4y = 2, y(0) = 1 can be solved using Laplace transforms. The Laplace transform of the differential equation is 5sY(s) + 4Y(s) = 2/s and the solution is Y(s) = 1/(5s+4). The inverse Laplace transform of Y(s) gives the solution of the differential equation as y(t) = e^-2t (1-2e^3t).

Solution in Laplace Transforms

We take the Laplace transform of both sides of the original differential equation:

• 5 (dy/dt) + 4y = 2, y(0) = 1
• 5sY(s) + 4Y(s) = 2/s

Solving the equation for Y(s) gives the solution as Y(s) = 1/(5s+4).

Inverse Laplace Transform

The inverse Laplace transform of Y(s) gives the solution of the differential equation as y(t) = e^-2t (1-2e^3t).

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