# Math Help - Differential by laplace

1. ## Differential by laplace

SOLVE X'-Y=e^t ,Y'+X=sint where X(0)=1 Y(0)=0

HERE DO I HAVE TO ELIMINATE X AND APPLY LAPLACE FOR Y PLEASE HELP

2. ## Re: Differential by laplace

Originally Posted by prasum
SOLVE X'-Y=e^t ,Y'+X=sint where X(0)=1 Y(0)=0

HERE DO I HAVE TO ELIMINATE X AND APPLY LAPLACE FOR Y PLEASE HELP
Apply the Laplace transform first. This will turn the system of ODE's into a system of algebraic equations.

$sX-1-Y=\frac{1}{s-1} \quad sY-0+X=\frac{1}{s^2+1}$

Now just eliminate either x or y and solve.

Thanks