Problem 1294 (difficulty: 7/10)

We know that \(\displaystyle f:\R^2\to\R\) is differentiable and

\(\displaystyle y^2\cdot D_1f(x,y) + x^3\cdot D_2f(x,y) = 0. \)

Prove that \(\displaystyle f(\sqrt2,\sqrt[3]3)=f(0,0)\).

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