What is the solution for 1/4 (d^2x)/(dt^2)+(dx)/(dt)+x=0 ?

The solution for 1/4 (d^2x)/(dt^2)+(dx)/(dt)+x=0 is x=c_{1}e^{-2t}+c_{2}te^{-2t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/4 (d^2x)/(dt^2)+(dx)/(dt)+x=0

\frac{1}{4} \frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 0

x = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t}

Solution steps

\frac{1}{4} \frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 0

Solve linear ODE:

x = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t}

x = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t}

9 y^{^{''}} - 18 y^{^{'}} + 34 y = 0

y^{^{''}} + \frac{49}{3} y = 0, y (0) = \frac{π}{8}, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + 10 y = 0, y (0) = 0, y^{^{'}} (0) = - 4

y^{^{''''}} + 2 y^{^{'''}} + y^{^{''}} + 8 y^{^{'}} - 12 y = 0

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (π) = 7, y (0) = 8

What is the solution for 1/4 (d^2x)/(dt^2)+(dx)/(dt)+x=0 ?
The solution for 1/4 (d^2x)/(dt^2)+(dx)/(dt)+x=0 is x=c_{1}e^{-2t}+c_{2}te^{-2t}