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PDE : Riemann's Method for Solving Cauchy Problem

Hello. Thanks for help! I will use * to indicate a partial derivative. For example, u*x denotes the partial derivative of u with respect to x. This is the probelm:

Use Riemann's method to solve the Cauchy problem:

u*xx + 4u*xy +3u*yy = 1, u=1 and u*n = square root of 5 times x, on the intial

curve y=2x.

If this problem is too difficult, then perhaps you may solve an easier one, just to give me some direction please. The only example I have is the Riemann function for the telegraph equation. It is very different form this question. Again, if this question is too difficult, then any example, along the same lines, will be fine.

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Solution Summary

Riemann's method is used to solve a Cauchy problem. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.