Question about the solution of the Burgers' equation.

Question

I have the equation $$u_t+uu_x-vu_{xx}=0$$ with $v>0$. The problem is to find the explicit form of the solution if is known that such solution have the form $u(x,t)=f(x-ct)$. \ I tried to solve it, but I only could do this $$\left(f-c\right)\frac{df}{dr}-v\frac{d^{2}f}{dr^{2}}=0$$ where $f(r)\equiv f(x-ct)$. But I don´t know how continue.