a) Find the general solution to the differential equation:

(Write the answer in a form such that its numerator is 1 and its integration constant is C)

$\displaystyle \frac{du}{dt} = u^3(t^3 - t) $

b) Find the particular solution of the above differential equation that satisfies the condition $\displaystyle u = 4 $ at $\displaystyle t = 0$