1. The problem statement, all variables and given/known data Find the general solution of the following equation ut + x2ux = t, u(x,0) = f(x), -inf < x < inf, t > 0 2. Relevant equations 3. The attempt at a solution Using method of characteristics I get du/dt = ut + dX/dtux = ux(dX/dt - x^2) + t so along the curve dX/dt = x^2 with x(0) = x0 we get x = -1/(t+x0) and x0 = -1/x - t So du/dt = t = -1/x - x0 so u(x,t) = -t/x - x0t + f(x0) so u(x,t) = t2 + f(-1/x - t) but when I check this I don't get the original PDE. Someone help.