What is the solution for y^'+xy=-x^3 ?

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

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y^'+xy=-x^3

y^{^{'}} + x y = - x^{3}

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

Solution steps

y^{'} (x) + x y = - x^{3}

Solve linear ODE:

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

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

\frac{d ^{2}}{d x ^{2}} (x^{5} e^{x})

y = 7 x

x \to - \infty lim (3^{x})

x \to 2 lim (- (\frac{x + 3}{x - 2}))

\int + \frac{sin ^{2} ( \frac{1}{t} )}{t ^{2}} d t

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