What is the solution for y^{''''}+10y^{''}+9y=0 ?

The solution for y^{''''}+10y^{''}+9y=0 is y=c_{1}cos(t)+c_{2}sin(t)+c_{3}cos(3t)+c_{4}sin(3t)

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y^{''''}+10y^{''}+9y=0

y^{^{''''}} + 10 y^{^{''}} + 9 y = 0

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

Solution steps

y^{(4)} (t) + 10 y^{''} (t) + 9 y = 0

Solve linear ODE:

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

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

What is the solution for y^{''''}+10y^{''}+9y=0 ?
The solution for y^{''''}+10y^{''}+9y=0 is y=c_{1}cos(t)+c_{2}sin(t)+c_{3}cos(3t)+c_{4}sin(3t)