# Laplace transform initial value problem

1. Dec 2, 2009

### jrsweet

1. The problem statement, all variables and given/known data

Use the Laplace transform to solve the following initial value problem:
x' = 7 x + 5 y, y'= -2 x + e5t, x(0)=0, y(0)=0

Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s)

2. Relevant equations

3. The attempt at a solution
I'm confused on how to deal with the the x and y in each equation. We didn't do an example like this in class so I'm a little lost. We did it with one equation, but not two. Any help would be greatly appreciated!

Last edited: Dec 3, 2009
2. Dec 3, 2009

### HallsofIvy

Staff Emeritus
Then take the Laplace transform of both x and y! It's exactly the same. You will get two equations for the two Laplace transforms. Solve for each transform, then take the inverse transform to find x and y. It might be a good idea to let the variable be the usual "s" in one transform and, say, "t" in the other.