What is the solution for t(dy)/(dt)+9y= 1/t ?

The solution for t(dy)/(dt)+9y= 1/t is y= 1/(8t)+(c_{1})/(t^9)

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t(dy)/(dt)+9y= 1/t

t \frac{d y}{d t} + 9 y = \frac{1}{t}

y = \frac{1}{8 t} + \frac{c _{1}}{t ^{9}}

Solution steps

t \frac{d y}{d t} + 9 y = \frac{1}{t}

Solve linear ODE:

y = \frac{1}{8 t} + \frac{c _{1}}{t ^{9}}

y = \frac{1}{8 t} + \frac{c _{1}}{t ^{9}}

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What is the solution for t(dy)/(dt)+9y= 1/t ?
The solution for t(dy)/(dt)+9y= 1/t is y= 1/(8t)+(c_{1})/(t^9)