Laplace transform initial value problem

[jrsweet]

Homework Statement

Use the Laplace transform to solve the following initial value problem:
x' = 7 x + 5 y, y'= -2 x + e^5t, 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)

Homework Equations

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!

 

[HallsofIvy]

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.