$$u u_x + (y + 1) u_y = u , x ∈ R, y > 0$$ $$u(x,0)=-3x, x ∈ R $$
I found the solution of the above initial value problem to be $$u(x,y)= \frac{-3x(y+1)}{(-3y+1)} $$
If someone could confirm this it would be fantastic. How do I sketch the characteristic base curves and define the region where the solution can be determined?