defence exam Army Havildar SAC Mock Test Series 2025 Mathematics Differential Equations

Solution of \(\frac{d y}{d x}=\left(1+x^{2}\right)\left(1+y^{2}\right)\) is:

1
\(\tan ^{-1} y=x+\frac{x^{3}}{3}+c\)
2
\(\tan ^{-1} y=x-\frac{x^{3}}{3}+c\)
3
\(\tan ^{-1} y=x^{2}+\frac{x^{3}}{3}+c\)
4
\( \tan ^{-1} y=x^{2}-\frac{x^{3}}{3}+c\)
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