What is the solution for y^'-xy=x^2e^{(x^2)/2} ?

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

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y^'-xy=x^2e^{(x^2)/2}

y^{^{'}} - x y = x^{2} e^{\frac{x ^{2}}{2}}

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

Solution steps

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

Solve linear ODE:

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

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

\int - \frac{3 x ^{2}}{32} + \frac{3 x}{8} d x

y = \frac{2 x + 1}{3 x - 4}

\frac{d}{d x} (e^{- \frac{x}{4}})

\int \frac{( x ^{2} )}{49 - x ^{2}} d x

y^{^{''}} - 9 y = 2 t^{2} + 3 t + 9

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