What is the solution for xy^2-2y^'y+y^'=0 ?

The solution for xy^2-2y^'y+y^'=0 is y=-1/(2\W(-(1){2e^{\frac{x^2-c_{1}+4)/4}})}

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xy^2-2y^'y+y^'=0

x y^{2} - 2 y^{^{'}} y + y^{^{'}} = 0

y = - \frac{1}{2 W ( - \frac{1}{2 e ^{\frac{x ^{2} - c _{1} + 4}{4}}} )}

Solution steps

x y^{2} - 2 y^{'} (x) y + y^{'} (x) = 0

Solve separable ODE:

y = - \frac{1}{2 W ( - \frac{1}{2 e ^{\frac{x ^{2} - c _{1} + 4}{4}}} )}

y = - \frac{1}{2 W ( - \frac{1}{2 e ^{\frac{x ^{2} - c _{1} + 4}{4}}} )}

\frac{d y}{d x} = \frac{y}{5}

d x = 6 \cdot 0.5 - 6 \cdot \frac{x}{50} d t

\frac{d y}{d t} = 0.07 (100 - y), y (0) = 25

y - 9 \frac{d y}{d t} = 0

\frac{d y}{d x} y = u, u = x^{2} + 2

What is the solution for xy^2-2y^'y+y^'=0 ?
The solution for xy^2-2y^'y+y^'=0 is y=-1/(2\W(-(1){2e^{\frac{x^2-c_{1}+4)/4}})}