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=xSolve 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
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