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ydx + x[logy/x]dy - 2xdy=0 solve using variable separable metho

vivek , 11 Years ago
Grade
anser 1 Answers
bharat bajaj

Last Activity: 11 Years ago

ydx + x[logy/x]dy - 2xdy=0
ydx -xdy +x[logy/x]dy -xdy = 0

divide by x^2
(ydx-xdy)/x^2 + (logy/x - 1)/x^2 . dy = 0
-d(y/x) +(logy/x-1)(y/x)^2 / y^2 .dy = 0
Take y/x=z
dz - (logz-1)z^2/y^2 dy = 0
dz(z^2)(logz-1) = dy/y^2
Now integrate it as the variables are separated and put z = y/x at the end.
Thanks
bharat Bajaj
IIT Delhi
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