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Solve the following differential equation dy/dx+ylogy/x-logy =0
By rearranging the give differential equation we get , dx/dy =1/y -x/(ylogy) dx/dy + x/(ylogy) =1/y Now, calculate the integrating factor (IF), e∫1/(ylogy)=I.F Taking, logy=t (say) differentiating on both sides we get, dy=ydt IF=e∫dt/t=elogt=t, where t=logy now, solving in linear differential equation form x(t)= ∫t/y dy, since dy=ydt xt = ∫t xt=t2/2 +cie x(logy)=(logy)2/2 =c
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