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

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

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

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

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

Solution steps

x \frac{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}}

e^{- x + 1} - x \cdot e^{- x + 1}

\int 14 sin^{3} (x) cos^{2} (x) d x

\int \frac{5 x}{x ^{3} + 1} d x

y^{^{'}} + 2 t y^{2} = 0, y (1) = \frac{1}{5}

x \to 0 + lim (\frac{1}{2 x})

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