Solve the differential equation `x (1 + y^2) dx - y (1 + x^2) dy = 0`, given that `y = 0`, when `x=1`

Answer

`(1+x^2)/(1+y^2)=c`

Explanation

We are given

`x (1 + y^2) dx - y (1 + x^2) dy = 0`

`x(1+y^2)dx=y(1+x^2)dy`

`x/(1+x^2)dx=y/(1+y^2)`


Taking Integration both sides we got,

`int x/(1+x^2)dx=int y/(1+y^2)`


Let us take `(1+x^2)=t` and `(1+y^2)=u`

Differentiating we get,

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