Suppose that m is a fixed positive integer. Show that the initial value problem:

$\displaystyle u' = u^\frac{2m}{2m+1}$, u(0)=0

has infinitely many continuously differentiable solutions.

I have solved the differential equation via the usual method of seperating variables, and have come up with the 2 solutions:

$\displaystyle u=(\frac{t}{2m+1})^{2m+1}$ and

$\displaystyle u=0$.

However clearly this is not an infinite number of solutions, so could someone point me in the direction of where to find the rest?

Thanks.