Question

Find the general solution of the differential equation


`(dy)/(dx) = (1 + {x}^(2) )(1 + {y}^(2) )`
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Answer 1

`{ \pink{ \tt{ { \tan }^( - 1) y - \frac{ {x}^(3) }{3} = c }}}`

Explanation:

This can be written as,

`{ \green{ \tt \frac{dy}{1 + {y}^(2)}}} = { \green{ \tt{(1 + {x}^(2))dx}}}`

Integeare on both sides, then

`{ \blue{ \tt{ ∫  \frac{1}{1 + {y}^(2)}}}}{ \blue{ \tt{dy}}} = { \blue{ \tt{  ∫ (1 + {x}^(2) )dx}}}`

`{ \blue{ \tt{ { \tan }^( - 1) y = \frac{ {x}^(3) }{3} + c}}}`

`{ \huge{ \green{ \blue{ \tt{ { \tan }^( - 1) y - \frac{ {x}^(3) }{3} = c}}}}}`