Question: Prove that there exist functions u(x, y), v(x, y), and w(X, y), and an r > 0 such that M.V.W are continuously differentiable and satisfy

Prove that there exist functions u(x, y), v(x, y), and w(X, y), and an r > 0 such that M.V.W are continuously differentiable and satisfy the equations

u + xv? - y + w = 0 v5 + yu? - x+ w = 0 w* + y - x* = 1

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