1. The problem statement, all variables and given/known data Solve the following IVP for 1st order quasilinear PDE s using the method of characteristics. u*u_x + y*u_y = x u = 2s, y = s, x = s 2. Relevant equations a(x,y,z)*u_x + b(x,y,z)*u_y = c(x,y,z) z = u(x_o,y_o) = 2s 3. The attempt at a solution The problem confuses me in the sense that this is the first one where x and y aren't coupled with their respective partial derivatives. for example I can solve x*u_x + y*u_y = x*u I'm just looking for more insight into the method of characteristics. does it imply that I can replace u with x with the parameters? back to the original problem u*u_x + y*u_y = x u = 2s, y = s, x = s is this an acceptable approach dx/dk = u and using the characteristic to write dx/dk = 2x (where s is the first parameter, and k the second one because the equation has 2 independent vars) dy/dk = y dz/dk = x this is the only part that confuses me and makes me believe im missing the bigger picture for this method. Thanks!