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Please answer question (b) 9. (a) Show that the PDE Ux = 0 has no solution...

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Advance Math

Please answer question (b)

9. (a) Show that the PDE Ux = 0 has no solution which is C1everywhere and satisfies the side condition u(x,x^3) = x , eventhough the side condition curve y = x^3 intersects each

characteristic line (y = d) only once.
(b) Part (a) demonstrates the necessity of the transversalitycondition on the intersections of the side condition curve with thecharacteristic lines. Explain why.

Hint. At what angle does the curve y = x^3 meet the x-axis?

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