I would like some help on comprehending this question as well as a push in the right direction. The question gave a system of first-order differential equation.
The question asked me to find the 2nd inhomogeneous equation that satisfies x(t). Does this mean the answer should all be in terms of x? I tried focusing on the x and differentiating it with respect to t.
for simplicity sake, I will write x(t) as x and y(t) as y.
After that step, I replaced the y' in the x'' equation with the rearranged y' from the original question into the differentiated x' equation. This gives:
this cancels down to:
but if you move everything to one side, it becomes
this is a second-order homogenous equation, so I don't quite know where I went wrong