9. Show that the initial value problemut+ux=xu(x, x) = 1has no solution. Give a reason for the problem.Note that the initial line in this case is NOT thexaxis (t= 0) but the linet=x.The ODEs aredxdt= 1,dudt=xand the initial condition for eachx(t=x) =ξ,u(x(t=x), t=x) = 1Solve the characteristic equationx=t+Kand use the initial conditionξ=ξ+KsoK= 0 and the characteristic isx=tThis is the only line, there is no family as in other problems.Substitute in the
This is the end of the preview.
access the rest of the document.
Constant of integration, Boundary value problem, initial condition