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6. Find the general solution:

$\frac{dy}{dx} = (1+x^2)(1+y^2)$

Answers (1)

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Given, in the question

$\frac{dy}{dx} = (1+x^2)(1+y^2)$

$\\ \implies \int \frac{dy}{(1+y^2)} = \int (1+x^2)dx$

$(\int \frac{dx}{(1+x^2)} =tan^{-1}x +c)$

$\\ \implies tan^{-1}y = x+\frac{x^3}{3} + C$

Posted by

HARSH KANKARIA

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