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Question
Solve: (1 – x) dy – (1 + y) dx = 0
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Solution
(1 – x) dy = (1 + y) dx
`("d"y)/((1 + y)) = ("d"x)/((1 - x))`
Integrating on both sides
`int ("d"y)/((1 + y)) = int ("d"x)/((1 - x))`
`int ("d"y)/((1 + y)) = - int (- "d"x)/((1 - x))`
`log (1 + y) = - log (1 - x) + log "c"`
`log (1 + y) = log ("c"/((1 - x)))`
⇒ `(1 + y) = "c"/((1 - x))`
∴ `(1 - x)(1 + y)` = c
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