What is the solution for y^{'''}+8y^{''}+52y^'=0 ?

The solution for y^{'''}+8y^{''}+52y^'=0 is y=c_{1}+e^{-4t}(c_{2}cos(6t)+c_{3}sin(6t))

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y^{'''}+8y^{''}+52y^'=0

y^{^{'''}} + 8 y^{^{''}} + 52 y^{^{'}} = 0

y = c_{1} + e^{- 4 t} (c_{2} cos (6 t) + c_{3} sin (6 t))

Solution steps

y^{'''} (t) + 8 y^{''} (t) + 52 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + e^{- 4 t} (c_{2} cos (6 t) + c_{3} sin (6 t))

y = c_{1} + e^{- 4 t} (c_{2} cos (6 t) + c_{3} sin (6 t))

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What is the solution for y^{'''}+8y^{''}+52y^'=0 ?
The solution for y^{'''}+8y^{''}+52y^'=0 is y=c_{1}+e^{-4t}(c_{2}cos(6t)+c_{3}sin(6t))