So I know how to solve linear partial differential equations but I am stuck on this new type of problem that is a nonlinear pde. The question is:
Determine the solution of $\frac{\partial \rho}{\partial t}=\rho^2$ which satisfies $\rho (x,0)=\sin x$.
Wolframalpha says the solution to this is $\frac{1}{c_1 - t}$ but then does that mean $c_1 = \frac{1}{\sin(x)}$?
Maple gives: $$\rho(x,t)=-\dfrac{\sin(x)}{\sin(x)\cdot t-1},$$ so yes $c_1=\dfrac 1{\sin(x)}$.