# Use of laplace to solve a differential equation

1. Dec 18, 2009

### hallic

I was asked to use a laplace transform to solve d^2x/dt^2 - 3(dx/dt) - 10x = e^-t
with the initial conditions x(0) = 0 and x'(0) = 0

I got down to (s^2)x(s) - sx(0) - x'(0) - 3(sX(0) - x(0)) - 10X =1/(s+1)

I tried plugging in the initail conditions and didnt get the answer I was supposed to, think I have gone wrong somewhere if someone can help me out

2. Dec 18, 2009

### gato_

Got it wrong. That's:
$$s^{2}X(s)-sx_{0}-x'_{0}-3(sX(s)-x_{0})-10X(s)=1/(s+1)$$
With the boundary conditions, you get
$$X(s)=\frac{1}{(s+1)(s^{2}-3s-10)}$$