Question

I need help with Laplace Transforms.
Solve the system:
x'+2y'+x=0 x'-y'+y=0 x(0)=0 y(0)=1

I got to the part where sX+2sY+X-2=0 and
sX-sY+Y+1=0

How do I solve the system from here?
thanks!

Answer 1

You have \(sX+2sY+X-2=0\) and \(sX-sY+Y+1=0\)

Answer 2

Solve them as you do with any other system of equation, either by substitution or elimination.

Answer 3

Your variables here are X and Y.

Answer 4

\[\left\{X=-\frac{2}{3 s^2-1},Y=-\frac{-3 s-1}{3 s^2-1}\right\} \]