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

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

Answers (1)

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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