CUET · MATHS · PYQ PAPER 2023
Solution of \(\frac{d y}{d x}=\left(1+x^2\right)\left(1+y^2\right)\) is :
- A \(\tan ^{-1} y=x+\frac{x^3}{3}+c\)
- B \(\tan ^{-1} y=x-\frac{x^3}{3}+c\)
- C \(\tan ^{-1} y=x^2+\frac{x^3}{3}+c\)
- D \(\tan ^{-1} y=x^2-\frac{x^3}{3}+c\)
Answer & Solution
Correct Answer
(A) \(\tan ^{-1} y=x+\frac{x^3}{3}+c\)
Step-by-step Solution
Detailed explanation
\(\int \frac{dy}{1+y^2} = \int (1+x^2)dx\) \(\tan^{-1} y = x + \frac{x^3}{3} + C\)
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