Hi. I finished solving a system of DEs using Laplace transform some time ago. The values I figured do not solve the system when plugged back into the original. However, I cannot find my error. I am sure it is something small, but I have been laboring for over an hour and cannot find where I went wrong. I feel like I've double-checked everything, but that cannot be so because the answers do not check.

The problem:

Solve the following for

[tex]v(0)=2[/math

] (*)
My solution:

My work:

Laplace transform the system to get:

,

(**)
simplifying,

solving for U(s), V(s)

partial fractions to inverse laplace later

inverse laplace, obtaining u(t), v(t)

simplify and you get what I wrote above.

The problem is, when I plug them into the system, both equations work out to 0...the second one is not equal to 2.

I have poured over this and cannot figure it out.

Can someone spot my error?

Thanks