What is the solution for (d^2x)/(dt^2)+12(dx)/(dt)+32x=0 ?

The solution for (d^2x)/(dt^2)+12(dx)/(dt)+32x=0 is x=c_{1}e^{-4t}+c_{2}e^{-8t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2x)/(dt^2)+12(dx)/(dt)+32x=0

\frac{d ^{2} x}{d t ^{2}} + 12 \frac{d x}{d t} + 32 x = 0

x = c_{1} e^{- 4 t} + c_{2} e^{- 8 t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 12 \frac{d x}{d t} + 32 x = 0

Solve linear ODE:

x = c_{1} e^{- 4 t} + c_{2} e^{- 8 t}

x = c_{1} e^{- 4 t} + c_{2} e^{- 8 t}

y^{^{'''}} - 16 y = 0

y^{^{''}} + a \cdot y^{^{'}} + b \cdot y = 0

(3440.3669700000000 \dots) y^{^{''}} + (0) y^{^{'}} + (22500) y = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = - \frac{6}{5}, y^{^{'}} (0) = - 3

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

What is the solution for (d^2x)/(dt^2)+12(dx)/(dt)+32x=0 ?
The solution for (d^2x)/(dt^2)+12(dx)/(dt)+32x=0 is x=c_{1}e^{-4t}+c_{2}e^{-8t}