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Question
Solve the differential equation: (x + 1) dy – 2xy dx = 0
Solution
(x + 1) dy - 2xy dx = 0
`("dy")/("dx") = (2"xy")/(x + 1)`
`(1)/(y) "dy" = (( 2x)/ (x+1)) dx`
`(1)/(y) "dy" = (( 2x + 2 - 2)/ (x+1)) dx`
`(1)/(y) "dy" = [ (2( x+ 1)) /((x + 1)) - (2)/((x+1))] dx`
`int_ (1)/(y) "dy" = int_ 2dx - int_ (2)/((x+1)) dx`
log | y | = 2x - 2 log | x - 1 | + c
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