What is the solution for y^{'''}+3y^{''}-54y=0 ?

The solution for y^{'''}+3y^{''}-54y=0 is y=c_{1}e^{3t}+e^{-3t}(c_{2}cos(3t)+c_{3}sin(3t))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{'''}+3y^{''}-54y=0

y^{^{'''}} + 3 y^{^{''}} - 54 y = 0

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

Solution steps

y^{'''} (t) + 3 y^{''} (t) - 54 y = 0

Solve linear ODE:

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

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

y^{^{'''}} - 3 y^{^{''}} = 0

y^{^{'''}} - 6 y^{^{''}} - 36 y^{^{'}} + 216 y = 0

4 y^{^{''}} - 8 y^{^{'}} + 5 y = 0

y^{^{''}} - 2 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} + 4 y = 0, y (\frac{π}{6}) = 5, y (0) = - 2

What is the solution for y^{'''}+3y^{''}-54y=0 ?
The solution for y^{'''}+3y^{''}-54y=0 is y=c_{1}e^{3t}+e^{-3t}(c_{2}cos(3t)+c_{3}sin(3t))