What is the solution for y^{''}+5y^'+6y=24e^t+36t^2 ?

The solution for y^{''}+5y^'+6y=24e^t+36t^2 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+2e^t+6t^2-10t+19/3

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y^{''}+5y^'+6y=24e^t+36t^2

y^{^{''}} + 5 y^{^{'}} + 6 y = 24 e^{t} + 36 t^{2}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + 2 e^{t} + 6 t^{2} - 10 t + \frac{19}{3}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 24 e^{t} + 36 t^{2}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + 2 e^{t} + 6 t^{2} - 10 t + \frac{19}{3}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + 2 e^{t} + 6 t^{2} - 10 t + \frac{19}{3}

y^{^{'''}} + y^{^{'}} = - 2 + 2 sin (x)

y^{^{''}} - 2 y^{^{'}} + 2 = 0

y^{^{''}} - 2 y^{^{'}} + 82 y = e^{x} cos (9 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 5 e^{4 x}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 6

What is the solution for y^{''}+5y^'+6y=24e^t+36t^2 ?
The solution for y^{''}+5y^'+6y=24e^t+36t^2 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+2e^t+6t^2-10t+19/3