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" The solution of the equation "xdy=(y+x...

" The solution of the equation "xdy=(y+x(f(y/x))/(f(y/x)))dx" is "

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If any differentisl equation in the form f(f_(1)(x,y)d(f_(1)(x,y)+phi(f_(2)(x,y)d(f_(2)(x,y))+....=0 then each term can be intergrated separately. For example, intsinxyd(xy)+int((x)/(y))d((x)/(y))=-cos xy+(1)/(2)((x)/(y))^(2)+C The solution of the differential equation (xy^(4)+y)dx-xdy=0 is