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Explain solution for  RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 34 maths textbook solution.

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Answer : \text { (d) } \tan ^{-1} y+\tan ^{-1} x=\tan ^{-1} C

Hint: Use variable separable equation i.e. take x terms to one side and y terms to the other side.

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

Explanation : \left(x^{2}+1\right) \frac{d y}{d x}=-\left(y^{2}+1\right)

\Rightarrow \frac{d y}{y^{2}+1}=-\frac{d x}{x^{2}+1}

Integrate both sides

\begin{aligned} &\Rightarrow \tan ^{-1} y=-\tan ^{-1} x+\tan ^{-1} C \\ &\Rightarrow \tan ^{-1} y+\tan ^{-1} x=\tan ^{-1} C \end{aligned}


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