What is the solution for x^2(dy)/(dx)+xy=x^3+1 ?

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

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x^2(dy)/(dx)+xy=x^3+1

x^{2} \frac{d y}{d x} + x y = x^{3} + 1

y = \frac{x ^{2}}{3} + \frac{ln ( x )}{x} + \frac{c _{1}}{x}

Solution steps

x^{2} \frac{d y}{d x} + x y = x^{3} + 1

Solve linear ODE:

y = \frac{x ^{2}}{3} + \frac{ln ( x )}{x} + \frac{c _{1}}{x}

y = \frac{x ^{2}}{3} + \frac{ln ( x )}{x} + \frac{c _{1}}{x}

\frac{d}{d x} (2 x + 6)

x \to \infty lim (\frac{x}{x ^{3} + 6})

\frac{\partial}{\partial x} (ln (x + z))

\int 5 sin (6 x) + 6 sin (5 x) d x

\frac{d}{d x} ((x - 2)^{3} (x - 1))

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