What is the solution for y^{'''}+y^{''}+y^'-39y=0 ?

The solution for y^{'''}+y^{''}+y^'-39y=0 is y=c_{1}e^{3t}+e^{-2t}(c_{2}cos(3t)+c_{3}sin(3t))

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y^{'''}+y^{''}+y^'-39y=0

y^{^{'''}} + y^{^{''}} + y^{^{'}} - 39 y = 0

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

Solution steps

y^{'''} (t) + y^{''} (t) + y^{'} (t) - 39 y = 0

Solve linear ODE:

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

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

What is the solution for y^{'''}+y^{''}+y^'-39y=0 ?
The solution for y^{'''}+y^{''}+y^'-39y=0 is y=c_{1}e^{3t}+e^{-2t}(c_{2}cos(3t)+c_{3}sin(3t))