dydr = (1+x2 ) (1+y2)6.

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Solution

The given differential equation is,

dy dx =( 1+ x 2 )( 1+ y 2 )

Separate the variables.

dy ( 1+ y 2 ) =( 1+ x 2 )dx

Integrating both the sides, we get,

∫ dy ( 1+ y 2 ) = ∫ ( 1+ x 2 )dx tan −1 y=x+ x 3 3 +C

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