I have to solve 3 * du/dx - 4*du/dy + u = 1 + x/3

with initial condition u(0,y)= y ^2 using the method of characteristics

The above derivatives are partial derivatives

My working until now:

Writing the characteristic equations: dx/ds = 3 => x=3s+x(0)

dy/ds = -4 => y=-4s + y(0)

and du/ds = 1- u + x/3

I am not sure how to proceed with the equation du/ds and so to proceed the exercise.

May someone help me please?

Thank you!