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

The solution for (dy)/(dx)+(3/x)y=-x-5 is y=-(x^2)/5-(5x)/4+(c_{1})/(x^3)

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(dy)/(dx)+(3/x)y=-x-5

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

y = - \frac{x ^{2}}{5} - \frac{5 x}{4} + \frac{c _{1}}{x ^{3}}

Solution steps

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

Solve linear ODE:

y = - \frac{x ^{2}}{5} - \frac{5 x}{4} + \frac{c _{1}}{x ^{3}}

y = - \frac{x ^{2}}{5} - \frac{5 x}{4} + \frac{c _{1}}{x ^{3}}

x \to 0 lim (\frac{sin ( 1 )}{1})

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

\frac{\partial}{\partial h} (\frac{m}{h ^{2}})

9 x + 2 x^{2}

\frac{d}{d x} (x^{- 12})

What is the solution for (dy)/(dx)+(3/x)y=-x-5 ?
The solution for (dy)/(dx)+(3/x)y=-x-5 is y=-(x^2)/5-(5x)/4+(c_{1})/(x^3)