What is the solution for y^{''''}=81y ?

The solution for y^{''''}=81y is y=c_{1}e^{3t}+c_{2}e^{-3t}+c_{3}cos(3t)+c_{4}sin(3t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''''}=81y

y^{^{''''}} = 81 y

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

Solution steps

y^{(4)} (t) = 81 y

Solve linear ODE:

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

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

y^{^{''}} + 16 y^{^{'}} + 8 y = 0

y^{^{''}} + y^{^{'}} - 2 y = 0, y^{0} = 1, y^{^{'}} 0 = 1

y^{^{''''}} - 9 y^{^{''}} + 4 y^{^{'}} + 12 y = 0

9 y^{^{''}} + 12 y^{^{'}} + 29 y = 0, y (0) = 1, y^{^{'}} (1) = 3

(D^{4} + 2 D^{2} + 1) y = 0

What is the solution for y^{''''}=81y ?
The solution for y^{''''}=81y is y=c_{1}e^{3t}+c_{2}e^{-3t}+c_{3}cos(3t)+c_{4}sin(3t)