Use the Laplace transform to solve the following initial value problem: y"- 3y + 2y = -5exp(t), y(0) = -4, y'(10) = 7.

First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)} You do not need to perform partial fraction decomposition yet.

L{y(t)}(s) = -5/[(s-1) (2 - 3s +2)] - (45-3)/(2 - 3s+2)