What is the solution for y^'+y(1-2x)=-(x^2)/2 y ?

The solution for y^'+y(1-2x)=-(x^2)/2 y is y=e^{-(x^3)/6+x^2-x+c_{1}}

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y^'+y(1-2x)=-(x^2)/2 y

y^{^{'}} + y (1 - 2 x) = - \frac{x ^{2}}{2} y

y = e^{- \frac{x ^{3}}{6} + x^{2} - x + c_{1}}

Solution steps

y^{'} (x) + y (1 - 2 x) = - \frac{x ^{2}}{2} y

Solve separable ODE:

y = e^{- \frac{x ^{3}}{6} + x^{2} - x + c_{1}}

y = e^{- \frac{x ^{3}}{6} + x^{2} - x + c_{1}}

y = e^{\frac{1}{x ^{2}}} + \frac{1}{e ^{x^{2}}}

\frac{d}{d x} (\frac{2 x}{x + 20})

y d y = - x d x

\frac{\partial}{\partial x} (x^{2} - 0.1 \cdot cos (6 \cdot x))

\frac{d y}{d x} = 3 + e^{- 3 x + y + 4}

What is the solution for y^'+y(1-2x)=-(x^2)/2 y ?
The solution for y^'+y(1-2x)=-(x^2)/2 y is y=e^{-(x^3)/6+x^2-x+c_{1}}