What is the solution for y^{''''}+k^2y^{''}=0 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''''}+k^2y^{''}=0

y^{^{''''}} + k^{2} y^{^{''}} = 0

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

Solution steps

y^{(4)} (t) + k^{2} y^{''} (t) = 0

Solve linear ODE:

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

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

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

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = 0

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 0

2 y^{^{''''}} + 11 y^{^{'''}} + 18 y^{^{''}} + 4 y^{^{'}} - 8 y = 0

3 y^{^{''}} - 5 y^{^{'}} + 2 y = 0

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