; x(0)=o, x'(0)=2, y(0)=0

Thank you for helping me understand how to solve this system of equations!!!

2. Originally Posted by Bananna
; x(0)=o, x'(0)=2, y(0)=0

Thank you for helping me understand how to solve this system of equations!!!
Here is the first one

Taking the transform of both sides gives

$s^2X-2+3sY+3Y=0$

and
$s^2X-2+3Y=\frac{1}{(s+1)}$

Now we have a system of Algebraic equaions. So isolate Y is the 2nd equation to get

$3sY=-\frac{1}{s+1} \iff Y= -\frac{1}{3}\left( \frac{1}{s(s+1)}\right)$

Taking the inverse transform (by any method you know)

Here is using the convolution theorem we get

$y(t)=-\frac{1}{3} \int_{0}^{t}e^{-\tau}d\tau=-\frac{1}{3}\left( -e^{-t}+1\right)$

This should get you started. Good luck.

3. You got me just where I needed to be, that wasn't difficult thanks for the help!