Question: Find conditions on a point (x0, y0, u0, v0) such that there exist real-valued functions u(x, y) and v(x, y) which are continuously differentiable near

Find conditions on a point (x0, y0, u0, v0) such that there exist real-valued functions u(x, y) and v(x, y) which are continuously differentiable near (x0, y0) and satisfy the simultaneous equations
xu2 + yv2 + xy = 9
xv2 + yu2 - xy = 7.

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Let Fx y u v xu 2 yv 2 xy 9 xv 2 yu 2 xy 7 and observe that Thus by ... View full answer

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