I'm preparing for the final in my ODE course by reviewing some past exams and I found this problem.
Solve the following equation by the separation of variables method.
I've learned that separable equations must be of the form
I've tried and failed to get the problem into the form of the product of a function of $x$ and a function of $t$. I can rearrange it to get
Can someone please show me how to solve this equation using the separation of variables method?