I must solve . I don't think it's separable, due to the 1 on the right side of the equation.
So I used the IF method, with no success.
My attempt:
The IF is . Multiplying the equation by it and integrating with respect to t, I reach .
I didn't know how to solve this integral and tried wolfram alpha, but the result involves the Gamma function and is pretty hard to reach I believe.
So what do I do?
Can I just say that ? It's not really under a nice form though. What do you think?