Integrate the following differential equation:

Make the substitution giving . Then we have,

Evaluating the integral on the left is a bit tricky (and I can’t find an exercise where we’ve already done it). For this integral we have,

But then, since

this integral is of the from so we have

Putting this back into where we left on our differential equation, we then have

This integral can be evaluated without the trick by substituting tan(t) instead of v, and then doing simple derivatives involving sec(t)