What is the solution for (d^2y)/(dt^2)+12(dy)/(dt)+36y=-4t+3 ?

The solution for (d^2y)/(dt^2)+12(dy)/(dt)+36y=-4t+3 is y=c_{1}e^{-6t}+c_{2}te^{-6t}-t/9+13/108

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(d^2y)/(dt^2)+12(dy)/(dt)+36y=-4t+3

\frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 36 y = - 4 t + 3

y = c_{1} e^{- 6 t} + c_{2} t e^{- 6 t} - \frac{t}{9} + \frac{13}{108}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 36 y = - 4 t + 3

Solve linear ODE:

y = c_{1} e^{- 6 t} + c_{2} t e^{- 6 t} - \frac{t}{9} + \frac{13}{108}

y = c_{1} e^{- 6 t} + c_{2} t e^{- 6 t} - \frac{t}{9} + \frac{13}{108}

y^{^{''}} - 2 y^{^{'}} = 4 x + e^{x}

y^{^{''}} + 2 y^{^{'}} = cos (t), y (0) = 0

y^{^{''}} + 7 y^{^{'}} = cos (2 x) + 8 e^{- 5 x}

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y^{^{'}} (0) = 0, y (0) = 0

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{2} t + 2 sin (t)

What is the solution for (d^2y)/(dt^2)+12(dy)/(dt)+36y=-4t+3 ?
The solution for (d^2y)/(dt^2)+12(dy)/(dt)+36y=-4t+3 is y=c_{1}e^{-6t}+c_{2}te^{-6t}-t/9+13/108