Show that the only solutions of the PDE xux +2yuy = 0 that are C and...

 

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Show that the only solutions of the PDE xux +2yuy = 0 that are C and defined for all (x, y) are the constant functions (e.g., u(x, y) = 5). Hint: Observe that the characteristic curves all issue from the origin. Show that the only solutions of the PDE xux +2yuy = 0 that are C and defined for all (x, y) are the constant functions (e.g., u(x, y) = 5). Hint: Observe that the characteristic curves all issue from the origin.