# Use the method of elimination to find a ODE satisfied by $x(t)$ and $y(t)$

$y''+x'-x+y = \sin t$

$x''+y'-x+y = e^t$

Any ideas?

-

## 1 Answer

Subtract the second equation from the first equation to get: $(y-x)''-(y-x)'=sin t-e^t$ Let z=y-x Solve this to get z then substitute y=x+z in one of the equations you gave.

-
How can I find z? –  user1038665 Nov 11 '12 at 23:46
Also, can the differential operator possibly be used to solve this problem? –  user1038665 Nov 11 '12 at 23:46