The question is
And I am supposed to solve for u.
The answer I got was
Is there a way I can solve for u?
Is there an initial condition so that you can get C ?
Because if C is 0, I have this factorisation :
Since you talked about and , we can assume that u and r are positive.
Thus the solutions are : u=r, or u=r=0 (for the second term, because it's always )