Question: By reformulating the problem as a Cauchy initial value problem find the parametric solutions of the partial differential equation u u /x + u /y

By reformulating the problem as a Cauchy initial value problem find the parametric solutions of the partial differential equation u u /x + u /y = 1, which contains the parabola x = 1, y^2 = 4y +8u 20 and discuss the existence and uniqueness of the solution.

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