Help with Method of Characteristics - PDE's

1. Oct 24, 2011

rexasaurus

1. Use the method of characteristics to solve: xux+yuy=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=uxdx/ds+uydy/ds=aux+buy
so a=x & b=y...

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 24, 2011

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=K2es
dy/ds=y integrate to get y=K3es

I am unsure how to use the IC's