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Question
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
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Solution
`(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
`(1 + x^2)/x "d"x = (1 + y)y "d"y`
`(1/x + x^2/x) "d"x = (y + y^2) "d"y`
⇒ `[1/x + x] "d"x = (y + y^2) "d"y`
Differentiating on both sides
`int (1/x + x) "d"x = int (y + y^2) "d"y`
⇒ `log x + x^2/2 = y^2/2 + y^3/3 + "c"`
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