The solution of the differential equation `x\ dx+y\ dy=x^2y\ dy-y^2x\ dx ,\ ` is a. `x^2-1=C(1+y^2)` b. `x^2+1=C(1-y^2)` c. `x^3-1=C(1+y^3)` d. `x^3+1=C(1-y^3)`

Explanation

A is correct answer

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Rightarrow x d x+x y^{2} d x=x^{2} y d y-y d y`

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Rightarrow x(1+y^{2}) d x=y(x^{2}-1) d y`

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Rightarrow int frac{2 x d x}{x^{2}-1} int frac{2 y}{1+y^{2}} d y+c`

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Rightarrow log (x^{2}-1)=log (1+y^{2})+log c`

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Rightarrow(x^{2}-1)=(1+y^{2}) c`

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