What is the solution for y^{''}+14y^'+49y=t-2e-7t ?

The solution for y^{''}+14y^'+49y=t-2e-7t is y=c_{1}e^{-7t}+c_{2}te^{-7t}-(6t)/(49)+(-14e+12)/(343)

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y^{''}+14y^'+49y=t-2e-7t

y^{^{''}} + 14 y^{^{'}} + 49 y = t - 2 e - 7 t

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} - \frac{6 t}{49} + \frac{- 14 e + 12}{343}

Solution steps

y^{''} (t) + 14 y^{'} (t) + 49 y = t - 2 e - 7 t

Solve linear ODE:

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} - \frac{6 t}{49} + \frac{- 14 e + 12}{343}

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} - \frac{6 t}{49} + \frac{- 14 e + 12}{343}

y^{^{''}} + 9 y = (x^{2} + 1) e^{3 x}

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- x} sin (2 x)

3 x^{^{''}} + 12 x = sin (2 t)

y^{^{''}} + 25 y = 2 sin (2 x), y (0) = 1, y^{^{'}} (0) = 0

y^{^{'''}} + 2 y^{^{''}} = 12 x + 4

What is the solution for y^{''}+14y^'+49y=t-2e-7t ?
The solution for y^{''}+14y^'+49y=t-2e-7t is y=c_{1}e^{-7t}+c_{2}te^{-7t}-(6t)/(49)+(-14e+12)/(343)