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

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

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(dy}{dx}+y(1-2x)=-\frac{x^2)/2 y

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

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

Solution steps

\frac{d y}{d 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}}

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