What is the solution for y^{'''}+5y^{''}+17y^'+13y=0 ?

The solution for y^{'''}+5y^{''}+17y^'+13y=0 is y=c_{1}e^{-t}+e^{-2t}(c_{2}cos(3t)+c_{3}sin(3t))

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y^{'''}+5y^{''}+17y^'+13y=0

y^{^{'''}} + 5 y^{^{''}} + 17 y^{^{'}} + 13 y = 0

y = c_{1} e^{- t} + e^{- 2 t} (c_{2} cos (3 t) + c_{3} sin (3 t))

Solution steps

y^{'''} (t) + 5 y^{''} (t) + 17 y^{'} (t) + 13 y = 0

Solve linear ODE:

y = c_{1} e^{- t} + e^{- 2 t} (c_{2} cos (3 t) + c_{3} sin (3 t))

y = c_{1} e^{- t} + e^{- 2 t} (c_{2} cos (3 t) + c_{3} sin (3 t))

(d^{3} + d) \cdot y = 0

2 y^{^{''}} + 4 y^{^{'}} - 6 y = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y^{^{'}} (0) = 0

f (x) \cdot f^{^{'}} (x) = 1 + 3 x, f (4) = 23

y^{^{'}} = - 12 y - 6, y (0) = 1

What is the solution for y^{'''}+5y^{''}+17y^'+13y=0 ?
The solution for y^{'''}+5y^{''}+17y^'+13y=0 is y=c_{1}e^{-t}+e^{-2t}(c_{2}cos(3t)+c_{3}sin(3t))