I know homework problems tend to be a bit unpopular on online forums, but I really need help with this problem since my college doesn't provide an answer to it. Also there seems to be no PDE Solver around on the web.
$$ \begin{cases} \dfrac {\partial u}{\partial t} +\dfrac {\partial u}{\partial x} +u=1 \\ u(x,0)=1 \end{cases} $$
I've attached a pic 1 of the partial differential equation that I'm talking about, my answer and the PDE are marked in red.
A simple yes or no would be greatly appreciated as an answer, I'm not asking for a detailed solution since I want to figure it out on my own, I'd just like to know if my answer is correct.
Thanks so much in advance!
link to the picture: https://i.stack.imgur.com/Z20M7.png