Integral of velocity if acceleration is a function of velocity

Question

I am having trouble taking the integral of this acceleration function:

$$a = (b - v^2)/c$$

where b and c are constants.

I cant seem to get the $dv$ and $dt$ on one side :(

If anyone can help me, please explain.

Thank you.

Answer 1

Write the equation as,

$$\frac{dv}{dt}= (b - v^2)/c$$

or,

$$\frac{dv}{b-v^2}= \frac 1c dt$$

Then, integrate

$$\int \frac{dv}{b-v^2}= \frac 1c \int dt$$