What is the solution for y^{''''}+8y^{''}+16y=0 ?

The solution for y^{''''}+8y^{''}+16y=0 is y=c_{1}cos(2t)+c_{2}sin(2t)+t(c_{3}cos(2t)+c_{4}sin(2t))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

y^{(4)} (t) + 8 y^{''} (t) + 16 y = 0

Solve linear ODE:

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

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

What is the solution for y^{''''}+8y^{''}+16y=0 ?
The solution for y^{''''}+8y^{''}+16y=0 is y=c_{1}cos(2t)+c_{2}sin(2t)+t(c_{3}cos(2t)+c_{4}sin(2t))