Problem: $dx/dt = x + y; dy/dt = y$
My try:
Since y is the derivative of itself, we have: $y = c_2e^t$
Now for x, let $D = d/dt$ Then we get the following: $Dx = x + y$ and $Dy = y$
Differentiating again we get: $D^2x = Dx + Dy$
Substituing the stuff back in we get $(D^2 - 2D + 1)x = 0$
Solving for gives us D = 1, giving: $x = c_1e^t$
This is where I get stuck, because x isnt finished yet, where do I go from here?
The final answer should be: $x = c_1e^t + c_2te^t$