What is the solution for y^{''}+6y^'+8y=16t+52 ?

The solution for y^{''}+6y^'+8y=16t+52 is y=c_{1}e^{-2t}+c_{2}e^{-4t}+2t+5

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y^{''}+6y^'+8y=16t+52

y^{^{''}} + 6 y^{^{'}} + 8 y = 16 t + 52

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + 2 t + 5

Solution steps

y^{''} (t) + 6 y^{'} (t) + 8 y = 16 t + 52

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + 2 t + 5

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + 2 t + 5

y^{^{''}} - y^{^{'}} - 6 y = 36 x, y (0) = 4, y^{^{'}} (0) = - 17

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

y^{^{''}} - y^{^{'}} = x^{2} + 2 x + 3

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 32 y = 6 + 3 x

y^{^{''}} + a y^{^{'}} - 2 a^{2} y = 1

What is the solution for y^{''}+6y^'+8y=16t+52 ?
The solution for y^{''}+6y^'+8y=16t+52 is y=c_{1}e^{-2t}+c_{2}e^{-4t}+2t+5