What is the solution for y^{'''}+5y^{''}+7y^'-13y=0 ?

The solution for y^{'''}+5y^{''}+7y^'-13y=0 is y=c_{1}e^t+e^{-3t}(c_{2}cos(2t)+c_{3}sin(2t))

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y^{'''}+5y^{''}+7y^'-13y=0

y^{^{'''}} + 5 y^{^{''}} + 7 y^{^{'}} - 13 y = 0

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

Solution steps

y^{'''} (t) + 5 y^{''} (t) + 7 y^{'} (t) - 13 y = 0

Solve linear ODE:

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

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

What is the solution for y^{'''}+5y^{''}+7y^'-13y=0 ?
The solution for y^{'''}+5y^{''}+7y^'-13y=0 is y=c_{1}e^t+e^{-3t}(c_{2}cos(2t)+c_{3}sin(2t))