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Prove that x^2-y^2=c(x^2+y^2)^2is the ...

Prove that `x^2-y^2=c(x^2+y^2)^2`is the general solution of differential equation `(x^3-3xy^2)dx=(y^3-3x^2y)dy`, where c is a parameter.

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To prove that \( x^2 - y^2 = c(x^2 + y^2)^2 \) is the general solution of the differential equation \( (x^3 - 3xy^2)dx = (y^3 - 3x^2y)dy \), we will follow these steps: ### Step 1: Differentiate the given equation We start with the equation: \[ x^2 - y^2 = c(x^2 + y^2)^2 \] Differentiating both sides with respect to \( x \): ...
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