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

The solution for x^{''''}+8x^{''}+16x=0 is x=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

Popular >

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y = x^{2} - 33, y = 7 - 3 x

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

\frac{1}{( x + 1 ) ^{2}}

\frac{d y}{d x} = \frac{( x - 2 )}{x}

(2 x^{2} + x + 1)^{- 3}

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