What is the solution for y^{''}+15y^'+50y=1296te^{-t} ?

The solution for y^{''}+15y^'+50y=1296te^{-t} is y=c_{1}e^{-5t}+c_{2}e^{-10t}+36te^{-t}-13e^{-t}

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y^{''}+15y^'+50y=1296te^{-t}

y^{^{''}} + 15 y^{^{'}} + 50 y = 1296 t e^{- t}

y = c_{1} e^{- 5 t} + c_{2} e^{- 10 t} + 36 t e^{- t} - 13 e^{- t}

Solution steps

y^{''} (t) + 15 y^{'} (t) + 50 y = 1296 t e^{- t}

Solve linear ODE:

y = c_{1} e^{- 5 t} + c_{2} e^{- 10 t} + 36 t e^{- t} - 13 e^{- t}

y = c_{1} e^{- 5 t} + c_{2} e^{- 10 t} + 36 t e^{- t} - 13 e^{- t}

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

y^{^{''}} + 9 y = cos (3 t) + sin (3 t)

50 x^{^{''}} + 1 0^{6} x = 10

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 H (t)

y^{^{''}} + 9 y = 12 cos (3 t), y (0) = 0, y^{^{'}} (0) = 6

What is the solution for y^{''}+15y^'+50y=1296te^{-t} ?
The solution for y^{''}+15y^'+50y=1296te^{-t} is y=c_{1}e^{-5t}+c_{2}e^{-10t}+36te^{-t}-13e^{-t}