What is the solution for y^{''}+7y^'+12y=-432t^3 ?

The solution for y^{''}+7y^'+12y=-432t^3 is y=c_{1}e^{-3t}+c_{2}e^{-4t}-36t^3+63t^2-(111t)/2+175/8

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y^{''}+7y^'+12y=-432t^3

y^{^{''}} + 7 y^{^{'}} + 12 y = - 432 t^{3}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} - 36 t^{3} + 63 t^{2} - \frac{111 t}{2} + \frac{175}{8}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 12 y = - 432 t^{3}

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} - 36 t^{3} + 63 t^{2} - \frac{111 t}{2} + \frac{175}{8}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} - 36 t^{3} + 63 t^{2} - \frac{111 t}{2} + \frac{175}{8}

y^{^{''}} + v y^{^{'}} = c e^{(- r^{2})}

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- 4 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 e^{- 5 t}

y^{^{''}} + 4 y^{^{'}} + 5 y = sin (5 t)

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 x - e^{- 4 x} + sin (2 x)

What is the solution for y^{''}+7y^'+12y=-432t^3 ?
The solution for y^{''}+7y^'+12y=-432t^3 is y=c_{1}e^{-3t}+c_{2}e^{-4t}-36t^3+63t^2-(111t)/2+175/8