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Question
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
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Solution
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
∴ x2 (1 - y) dy = - y2 (1 + x) dx
∴ `((1-y)/y^2)dy = - ((1+x)/x^2)dx`
Integrating on both sides, we get
`int(1/y^2- 1/y) dy = - int (1/x^2+1/x)dx`
∴ `-1/y - log |y| = - (-1/x + log | x |)+c`
∴`(-1)/y - log |y| = 1/x - log | x |+c`
∴ `log | x | - log | y | = 1/x + 1/y + c`
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