What is the solution for y^{''''}+5y^{''}+4y=0 ?

The solution for y^{''''}+5y^{''}+4y=0 is y=c_{1}cos(t)+c_{2}sin(t)+c_{3}cos(2t)+c_{4}sin(2t)

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y^{''''}+5y^{''}+4y=0

y^{^{''''}} + 5 y^{^{''}} + 4 y = 0

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

Solution steps

y^{(4)} (t) + 5 y^{''} (t) + 4 y = 0

Solve linear ODE:

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

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

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What is the solution for y^{''''}+5y^{''}+4y=0 ?
The solution for y^{''''}+5y^{''}+4y=0 is y=c_{1}cos(t)+c_{2}sin(t)+c_{3}cos(2t)+c_{4}sin(2t)