The differentials $dx/y^3$, $x\,dx/y^3$ and $dx/y^2$ of the quartic $x^4+y^4=2$ are linearly independent

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The differentials $dx/y^3$, $x\,dx/y^3$ and $dx/y^2$ of the quartic $x^4+y^4=2$ are linearly independent · Prove2Me