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ydx + x[logy/x]dy - 2xdy=0 solve using variable separable method?
ydx + x[logy/x]dy - 2xdy=0ydx -xdy +x[logy/x]dy -xdy = 0divide 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 = 0Take y/x=zdz - (logz-1)z^2/y^2 dy = 0dz(z^2)(logz-1) = dy/y^2Now integrate it as the variables are separated and put z = y/x at the end.Thanksbharat BajajIIT Delhiaskiitians faculty
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