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

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

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

y^{^{''}} + 9 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 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}

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = - 12 sec (3 t)

y^{^{''}} + 4 y = g (t), y (0) = 5, y^{^{'}} (0) = 16

x^{^{''}} - x = t

4 y^{^{''}} - 4 y^{^{'}} + y = 16 e^{\frac{1}{2} t}

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