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Solve the equation aux buy u 0 with cauchy data us e-s

Solve the equation aux + buy + u = 0 with Cauchy data u(s) = e-s along the straight lines (x(s),y(s)) = (cs,ds). The solution breaks down for a particular combination of a,b,c and d. Describe the combination geometrically and explain it in terms of characteristic curves.

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