Question

Solve the initial value problem below using the method of Laplace transforms. y"-8y' +41y=58e6⁶ᵗ, y(0) = 2, y'(0) = 17

Answer 1

To solve the initial value problem using the method of Laplace transforms, take the Laplace transform of both sides of the differential equation, substitute the initial conditions, and then take the inverse Laplace transform to obtain the solution.

Step-by-step explanation:

To solve the initial value problem using the method of Laplace transforms, we need to first take the Laplace transform of both sides of the differential equation. Applying the Laplace transform to the left-hand side, we get:

s^2Y(s) - sy(0) - y'(0) - 8sY(s) + 8y(0) + 41Y(s) = 58/(s-6)^2

Now, substitute the given initial conditions y(0) = 2 and y'(0) = 17 into the equation, and solve for Y(s).

Finally, take the inverse Laplace transform of Y(s) to obtain the solution y(t).