Integrating a non-separable differential equation

Question

I need to integrate

$$ dx = [k-\lambda x] dt / \tau $$

to solve for x(t), where k, $\lambda$, and $\tau$ are constants. However, the equation seems to be non-separable, so I'm not sure how to go about integrating it.

Answer 1

This equation is separable: $$\frac{1}{k-\lambda x} dx = \frac{1}{\tau}dt$$