What is the solution for y^{''}+8y^'+17y=0 ?

The solution for y^{''}+8y^'+17y=0 is y=e^{-4t}(c_{1}cos(t)+c_{2}sin(t))

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y^{''}+8y^'+17y=0

y^{^{''}} + 8 y^{^{'}} + 17 y = 0

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

Solution steps

y^{''} (t) + 8 y^{'} (t) + 17 y = 0

Solve linear ODE:

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

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

\frac{d}{d x} ((x^{3} + 1) (x^{2} - 3 x))

\frac{d ^{2}}{d x ^{2}} (x^{2} - \frac{1}{x ^{2}})

\int_{0}^{4} 2^{x} d x

\frac{d}{d x} (2 x^{3} + 3)

\int e^{t} d t

What is the solution for y^{''}+8y^'+17y=0 ?
The solution for y^{''}+8y^'+17y=0 is y=e^{-4t}(c_{1}cos(t)+c_{2}sin(t))