What is the solution for y^{''}+6y^'+8y=2t+e^t ?

The solution for y^{''}+6y^'+8y=2t+e^t is y=c_{1}e^{-2t}+c_{2}e^{-4t}+t/4-3/16+1/15 e^t

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y^{''}+6y^'+8y=2t+e^t

y^{^{''}} + 6 y^{^{'}} + 8 y = 2 t + e^{t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + \frac{t}{4} - \frac{3}{16} + \frac{1}{15} e^{t}

Solution steps

y^{''} (t) + 6 y^{'} (t) + 8 y = 2 t + e^{t}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + \frac{t}{4} - \frac{3}{16} + \frac{1}{15} e^{t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + \frac{t}{4} - \frac{3}{16} + \frac{1}{15} e^{t}

x^{^{''}} + 25 x = 2 cos (5.1 t)

y^{^{'''}} + 9 y^{^{''}} + 27 y^{^{'}} + 27 y = 9 e^{- 3 x}

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

y^{^{''}} + y^{^{'}} - 6 y = 10 e^{2 x} - 18 e^{3 x} - 6 x - 11

y^{^{''}} + y^{^{'}} = sec^{2} (x)

What is the solution for y^{''}+6y^'+8y=2t+e^t ?
The solution for y^{''}+6y^'+8y=2t+e^t is y=c_{1}e^{-2t}+c_{2}e^{-4t}+t/4-3/16+1/15 e^t