What is the solution for derivative of (xy)=(y)x ?

The solution for derivative of (xy)=(y)x is y=(e^{x+c_{1}})/x

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derivative of (xy)=(y)x

\frac{d}{d x} ((x) y) = (y) x

y = \frac{e ^{x + c_{1}}}{x}

Solution steps

\frac{d}{d x} ((x) y) = (y) x

Solve separable ODE:

y = \frac{e ^{x + c_{1}}}{x}

y = \frac{e ^{x + c_{1}}}{x}

\frac{d}{d x} (z (x) \cdot e^{2 x}) = e^{2 x}

e^{y} \cdot d y - 2 x \cdot d x = 0

\frac{d y}{d t} + 24 \cdot 1 0^{- 3} y = 384 \cdot 1 0^{- 3}

\frac{d y}{d x} (\frac{x ^{2}}{3 y ^{2}}) = 1

f (x) = \frac{1}{x ^{7}} \frac{df}{d x}

What is the solution for derivative of (xy)=(y)x ?
The solution for derivative of (xy)=(y)x is y=(e^{x+c_{1}})/x