What is the solution for yln(x)(xdy+ydx)=(xyln(x)-y)dy ?

The solution for yln(x)(xdy+ydx)=(xyln(x)-y)dy is y=e^{x+c_{1}}x^{-x}

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yln(x)(xdy+ydx)=(xyln(x)-y)dy

y ln (x) (x d y + y d x) = (x y ln (x) - y) d y

y = e^{x + c_{1}} x^{- x}

Solution steps

y ln (x) (x d y + y d x) = (x y ln (x) - y) d y

Solve separable ODE:

y = e^{x + c_{1}} x^{- x}

y = e^{x + c_{1}} x^{- x}

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What is the solution for yln(x)(xdy+ydx)=(xyln(x)-y)dy ?
The solution for yln(x)(xdy+ydx)=(xyln(x)-y)dy is y=e^{x+c_{1}}x^{-x}