What is the solution for y^{''''}-3y^{''}-4y=0 ?

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

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

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

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

Solution steps

y^{(4)} (t) - 3 y^{''} (t) - 4 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 0.5 y^{^{'}} + y = 0

y^{^{''}} + 64 π^{2} y = 0

y^{^{''}} + 16 y^{^{'}} + 73 y = 0, y^{^{'}} (0) = 8

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 4

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 7

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