Question

Solve listed initial value problems by using the Laplace Transform:

3.      y^ll + 4y = t − 1,    y(0) = 1, y^l(0) = −1

Answer 1

We will take the Laplace transform both sides of the given differential equation and then using that the Laplace transform of y(t) is Y(s), we have the Laplace transform of y" as s​​​​​​2​​​​​Y(s)-sy(0)-y'(0), putting these values in the the above equation and then using the rules, we will get the solution y(t) of the given initial value problem.  

The Step by step explanatory solution is provided below.