Solving Differential Equations: Simple equation help!!?

Question

I need to solve this differential equation.

dx/dt = x - (x^2)

The answer is x = (C*(e^t))/((C*(e^t)) - 1)

Can you help me figure out how to get from the problem to the answer?

Any help would be appreciated. Thank you!

Answer 1

assuming you can integrate...the problem is separable int { 1 / [x-x²]} dx =t + C