Prove that $x^{2} - y^{2} = c (x^{2} + y^{2})^{2}$ is the general solution of differential equation $(x^{3} - 2 x y^{2}) d x = (y^{3} - 3 x^{2} y) d y$ , where c is a parameter.

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Prove that

x^{2} - y^{2} = c (x^{2} + y^{2})^{2}

is the general solution of differential equation

(x^{3} - 2 x y^{2}) d x = (y^{3} - 3 x^{2} y) d y

, where c is a parameter.

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Question Text

Prove that

x^{2} - y^{2} = c (x^{2} + y^{2})^{2}

is the general solution of differential equation

(x^{3} - 2 x y^{2}) d x = (y^{3} - 3 x^{2} y) d y

, where c is a parameter.

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