y' = (y/x) + x/(x-y)
y = z + x --> z' + 1 = (z/x) + 1 - (x/z)
z' = (z/x) - (x/z)
z = wx --> w'x + w = w - 1/w
w'x = -1/w
w'w = -1/x
w^2 / 2 = C/2 - ln|x|
w = +- √( C - 2ln|x| )
z = wx = +- x √( C - 2ln|x| )
y = z + x = x +- x √( C - 2ln|x| )
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Answers & Comments
y' = (y/x) + x/(x-y)
y = z + x --> z' + 1 = (z/x) + 1 - (x/z)
z' = (z/x) - (x/z)
z = wx --> w'x + w = w - 1/w
w'x = -1/w
w'w = -1/x
w^2 / 2 = C/2 - ln|x|
w = +- √( C - 2ln|x| )
z = wx = +- x √( C - 2ln|x| )
y = z + x = x +- x √( C - 2ln|x| )