A problem that my friend gave me. I never took diff-e-q but my guess would be to integrate with respect to x then substitue x(0) to find the constant, but not sure if that's right, doesn't seem like diff-e-q material that way.

Separate variables and use partial fractions to solve the initial value problem $\displaystyle \frac{dt}{dx}=17x(x-15);x(0)=17$