# Differential by laplace

• February 23rd 2013, 05:12 AM
prasum
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
• February 23rd 2013, 02:11 PM
TheEmptySet
Re: Differential by laplace
Quote:

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.
• February 24th 2013, 01:09 AM
prasum
Re: Differential by laplace
Thanks