What is the solution for y^{'''}+y^{''}+y^'-3y=0 ?

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

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y^{'''}+y^{''}+y^'-3y=0

y^{^{'''}} + y^{^{''}} + y^{^{'}} - 3 y = 0

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

Solution steps

y^{'''} (t) + y^{''} (t) + y^{'} (t) - 3 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = - 5

y^{^{''}} + 6 y + 9 y = 0

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 0

y^{^{''}} + 8 y^{^{'}} + 9 y = 0, y (1) = 1, y^{^{'}} (1) = 0

2 y^{^{''}} - 4 y^{^{'}} + 3 y = 0

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