What is the solution for (dy}{dx}=\frac{xy+x)/y ?

The solution for (dy}{dx}=\frac{xy+x)/y is y=-\W(-1/(e^{(-c_{1)+x^2)/2}})-1

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(dy}{dx}=\frac{xy+x)/y

\frac{d y}{d x} = \frac{x y + x}{y}

y = - W (- \frac{1}{e ^{\frac{- c _{1} + x ^{2}}{2}}}) - 1

Solution steps

\frac{d y}{d x} = \frac{x y + x}{y}

Solve separable ODE:

y = - W (- \frac{1}{e ^{\frac{- c _{1} + x ^{2}}{2}}}) - 1

y = - W (- \frac{1}{e ^{\frac{- c _{1} + x ^{2}}{2}}}) - 1

x \to 1000 lim (x^{\frac{2}{3}})

\frac{d}{d x} (\frac{1}{3} x^{3} - 5 x - \frac{4}{x})

\int x \cdot ln^{5} (x) d x

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{x} + x e^{2 x}

f (x) = cot (x^{2})

What is the solution for (dy}{dx}=\frac{xy+x)/y ?
The solution for (dy}{dx}=\frac{xy+x)/y is y=-\W(-1/(e^{(-c_{1)+x^2)/2}})-1