What is the solution for (xdy)/(dx)+3y=x^3-x ?

The solution for (xdy)/(dx)+3y=x^3-x is y=(x^3)/6-x/4+(c_{1})/(x^3)

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(xdy)/(dx)+3y=x^3-x

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

y = \frac{x ^{3}}{6} - \frac{x}{4} + \frac{c _{1}}{x ^{3}}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{3}}{6} - \frac{x}{4} + \frac{c _{1}}{x ^{3}}

y = \frac{x ^{3}}{6} - \frac{x}{4} + \frac{c _{1}}{x ^{3}}

What is the solution for (xdy)/(dx)+3y=x^3-x ?
The solution for (xdy)/(dx)+3y=x^3-x is y=(x^3)/6-x/4+(c_{1})/(x^3)