Show that the differential equation representing one parameter family of curves `(x^2-y^2)=c(x^2+y^2)^2i s\ (x^3-3x y^2)dx=(y^3-3x^2y)dy`

Explanation

Given differential
equation

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

`frac{x^{3}-3 x y^{2}}{y^{3}-3 x^{2} y}=frac{d y}{d x} `

`frac{d y}{d x}=frac{x^{3}-3 x y^{2}}{y^{3}-3 x^{2} y}`

`frac{d y}{d x}=frac{x^{3}(1-frac{3 x y^{2}}{x^{3}})}{y^{3}(1-frac{3 x^{2} y}{y^{3}})}`

`frac{d y}{d x}=(frac{x}{y})^{3} times frac{(1-3(frac{y}{x})^{2})}{(1-3(frac{x}{y})^{2})} quad ldots(1)`


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