xy'-xsin(y/x)-y=0
let
u=y/x
du/dx = (1/x)dy/dx - (1/x^2)y
dy/dx = x[du/dx+ (1/x)u]
xy'-xsin(y/x)-y=0
x^2.[du/dx+ (1/x)u] - xsinu - xu =0
x^2.du/dx -xsinu =0
∫du/sinu = ∫dx/x
ln|cscu -cotu | = lnx +C'
cscu -cotu = Cx
csc(y/x) -cot(y/x) =Cx
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