Answer to Question #25828 in Differential Equations for Matthew Lind

Question

a) Solve the equation uu_x+u_y=1 with the initial condition u(x,x)=0. Hints: when finding the characteristic curves, solve for u before solving for x. When expressing t in terms of x and y, remember that t=0 on the initial curve.
b) Find the domain of the solution u(x,y) found in part a).