$(x^{2} + 2 x y - y^{2}) d x + (y^{2} + 2 x y - x^{2}) d x = 0$
Solve by Homogeneous.

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Solution

$(x^{2} + 2 x y - y^{2}) d x + (y^{2} + 2 x y - x^{2}) d x = 0 \Rightarrow (x^{2} + 2 x y - y^{2} + y^{2} + 2 x y - x^{2}) d x = 0 \Rightarrow 4 x y d x = 0$
Integrating with respect to $x$
$2 x^{2} (y) = k$

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