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  • Explain solution for RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 31 maths textbook solution.

Explain solution for  RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 31 maths textbook solution.

Answers (1)

Answer : \frac{x+y}{1-x y}=C

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

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{dy}{y^{2}+1}=-\frac{dx}{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 \\ &\Rightarrow \tan ^{-1}\left[\frac{x+y}{1-x y}\right]=\tan ^{-1} C \\ &\Rightarrow \frac{x+y}{1-x y}=C \end{aligned}

Note: Final answer is not matching

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