What is the solution for (xdy)/(dx)+5y=x^3-x ?

The solution for (xdy)/(dx)+5y=x^3-x is y=(x^3)/8-x/6+(c_{1})/(x^5)

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(xdy)/(dx)+5y=x^3-x

\frac{x d y}{d x} + 5 y = x^{3} - x

y = \frac{x ^{3}}{8} - \frac{x}{6} + \frac{c _{1}}{x ^{5}}

Solution steps

\frac{x d y}{d x} + 5 y = x^{3} - x

Solve linear ODE:

y = \frac{x ^{3}}{8} - \frac{x}{6} + \frac{c _{1}}{x ^{5}}

y = \frac{x ^{3}}{8} - \frac{x}{6} + \frac{c _{1}}{x ^{5}}

\int_{0}^{1} \frac{e ^{x} + 1}{e ^{x} + x} d x

y^{^{'}} = y sin (x), y (0) = 1

\frac{1}{6} y^{^{''}} + 6 y = tan (6 t) - \frac{1}{2} e^{3 t}

\frac{\partial}{\partial x} (tan (y))

\frac{d y}{d x} = \frac{( 2880 - y )}{320}

What is the solution for (xdy)/(dx)+5y=x^3-x ?
The solution for (xdy)/(dx)+5y=x^3-x is y=(x^3)/8-x/6+(c_{1})/(x^5)