What is the solution for (dy)/(dx)+xy=x^3 ?

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

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(dy)/(dx)+xy=x^3

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

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

Solution steps

\frac{d y}{d 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}}}

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