Help with Method of Characteristics - PDE's

[rexasaurus]

1. Use the method of characteristics to solve: xu_x+yu_y=1



2. given condition of u(x,y)=1 when x²+y²=1



3. I know I need to transpose into the s-t domain. Using: du/ds=u_xdx/ds+u_ydy/ds=au_x+bu_y
so a=x & b=y...

please help

 

[rexasaurus]

I was able to solve for the following:
du/ds=1 integrate to get u=s+K₁
dx/ds=x integrate to get x=K₂e^s
dy/ds=y integrate to get y=K₃e^s

I am unsure how to use the IC's