I am trying to solve this PDE using method of characteristics:
$u_y + 3u_x = -u^2, u(x,0)=f(x)$
This is how I started:
I then integrated these equations and got:
Next step, find $s$ and $u_0$. I let $y_0=0$ so $s=y$. To get my $u_0$:
Finally, I put $s$ and $u_0$ in my expression for $u$ to get the solution:
But that isn't the same solution as the one my professor got. I don't understand what I did wrong. Is there something wrong with my use of the initial condition?