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Question: Answered & Verified by Expert
The solution of the differential equation $\left(1+x^2\right) \frac{d y}{d x}=x$ is
MathematicsDifferential EquationsJEE Main
Options:
  • A $y=\tan ^{-1} x+c$
  • B $y=-\tan ^{-1} x+c$
  • C $y=\frac{1}{2} \log _e \left(1+x^2\right)+c$
  • D $y=-\frac{1}{2} \log _e\left(1+x^2\right)+c$
Solution:
2422 Upvotes Verified Answer
The correct answer is: $y=\frac{1}{2} \log _e \left(1+x^2\right)+c$
$\begin{aligned} & \left(1+x^2\right) \frac{d y}{d x}=x \Rightarrow d y=\frac{x}{1+x^2} d x \\ & \Rightarrow \int d y=\int \frac{x}{1+x^2} d x+c \Rightarrow y=\frac{1}{2} \log _e\left(1+x^2\right)+c\end{aligned}$

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