What is the solution for y^{''''}+16y^{''}=0 ?

The solution for y^{''''}+16y^{''}=0 is y=c_{1}+c_{2}t+c_{3}cos(4t)+c_{4}sin(4t)

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y^{''''}+16y^{''}=0

y^{^{''''}} + 16 y^{^{''}} = 0

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

Solution steps

y^{(4)} (t) + 16 y^{''} (t) = 0

Solve linear ODE:

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

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

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

\frac{d ^{2} q}{d t ^{2}} + \frac{d q}{d t} + q = 0

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = - 8, y^{^{'}} (0) = - 1

y^{^{''}} + 18 y = 0, y (0) = - 3, y^{^{'}} (0) = - 1

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 6 y = 0

What is the solution for y^{''''}+16y^{''}=0 ?
The solution for y^{''''}+16y^{''}=0 is y=c_{1}+c_{2}t+c_{3}cos(4t)+c_{4}sin(4t)