What is the solution for y^{''}+8y^'+17y=2e^{-4t}cos(t) ?

The solution for y^{''}+8y^'+17y=2e^{-4t}cos(t) is y=e^{-4t}(c_{1}cos(t)+c_{2}sin(t))+e^{-4t}tsin(t)

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y^{''}+8y^'+17y=2e^{-4t}cos(t)

y^{^{''}} + 8 y^{^{'}} + 17 y = 2 e^{- 4 t} cos (t)

y = e^{- 4 t} (c_{1} cos (t) + c_{2} sin (t)) + e^{- 4 t} t sin (t)

Solution steps

y^{''} (t) + 8 y^{'} (t) + 17 y = 2 e^{- 4 t} cos (t)

Solve linear ODE:

y = e^{- 4 t} (c_{1} cos (t) + c_{2} sin (t)) + e^{- 4 t} t sin (t)

y = e^{- 4 t} (c_{1} cos (t) + c_{2} sin (t)) + e^{- 4 t} t sin (t)

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} + 26 x e^{x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} 4 + 8 y = 8 x^{2}

y^{^{''}} - 2 y^{^{'}} = x^{2} - 1

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = sin (x)

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

What is the solution for y^{''}+8y^'+17y=2e^{-4t}cos(t) ?
The solution for y^{''}+8y^'+17y=2e^{-4t}cos(t) is y=e^{-4t}(c_{1}cos(t)+c_{2}sin(t))+e^{-4t}tsin(t)