What is the solution for (dy)/(dx)+1/(x+8)y=x^{-2} ?

The solution for (dy)/(dx)+1/(x+8)y=x^{-2} is y=(ln(x))/(x+8)-8/(x(x+8))+(c_{1})/(x+8)

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(dy)/(dx)+1/(x+8)y=x^{-2}

\frac{d y}{d x} + \frac{1}{x + 8} y = x^{- 2}

y = \frac{ln ( x )}{x + 8} - \frac{8}{x ( x + 8 )} + \frac{c _{1}}{x + 8}

Solution steps

\frac{d y}{d x} + \frac{1}{x + 8} y = x^{- 2}

Solve linear ODE:

y = \frac{ln ( x )}{x + 8} - \frac{8}{x ( x + 8 )} + \frac{c _{1}}{x + 8}

y = \frac{ln ( x )}{x + 8} - \frac{8}{x ( x + 8 )} + \frac{c _{1}}{x + 8}

What is the solution for (dy)/(dx)+1/(x+8)y=x^{-2} ?
The solution for (dy)/(dx)+1/(x+8)y=x^{-2} is y=(ln(x))/(x+8)-8/(x(x+8))+(c_{1})/(x+8)