What is the solution for y^{''}+9*y^'=5t ?

The solution for y^{''}+9*y^'=5t is y=c_{1}+c_{2}e^{-9t}+(5t^2)/(18)-(5t)/(81)

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y^{''}+9*y^'=5t

y^{^{''}} + 9 \cdot y^{^{'}} = 5 t

y = c_{1} + c_{2} e^{- 9 t} + \frac{5 t ^{2}}{18} - \frac{5 t}{81}

Solution steps

y^{''} (t) + 9 \cdot y^{'} (t) = 5 t

Solve linear ODE:

y = c_{1} + c_{2} e^{- 9 t} + \frac{5 t ^{2}}{18} - \frac{5 t}{81}

y = c_{1} + c_{2} e^{- 9 t} + \frac{5 t ^{2}}{18} - \frac{5 t}{81}

What is the solution for y^{''}+9*y^'=5t ?
The solution for y^{''}+9*y^'=5t is y=c_{1}+c_{2}e^{-9t}+(5t^2)/(18)-(5t)/(81)