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

Explanation

Given: `(1+x^{2}) frac{d y}{d x}+(1+y^{2})=0`

FInd: Find the particular solution of this differential equation.

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

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

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

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Integrating both side,

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