What is the solution for y(dy)/(dx)=x-yx ?

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

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y(dy)/(dx)=x-yx

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

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

Solution steps

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

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 sin (y) + (x^{2} + 1) cos (y) y^{^{'}} = 0

x^{2} (x d y + y d x) = 7 x d y - 7 y d x

e^{x} y \frac{d y}{d x} = e^{- y} + \frac{e ^{- 2 x}}{e ^{y}}

y^{^{'}} sin (x) = y ln (y), y (\frac{π}{2}) = e

\frac{d y}{d x} + x^{2} y = 3 x^{2}

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