The solution of the differential equation `(1+x^2)(dy)/(dx)+1+y^2=0,` is a. `tan^(-1)x-tan^(-1)y=tan^(-1)C` b. `tan^(-1)y-tan^(-1)x=tan^(-1)C` c. `tan^(-1)y+-tan^(-1)x=tan^(\ )C` d.`tan^(-1)y+tan^(-1)x=tan^(-1)C`

Explanation

D is right answer


`(1+x^{2}) d y / d x+1+y^{2}=0 `

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



After using variable separable we obtain ,

`

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


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