What is the solution for (d^2x)/(dt^2)+2(dx)/(dt)+8x=0 ?

The solution for (d^2x)/(dt^2)+2(dx)/(dt)+8x=0 is x=e^{-t}(c_{1}cos(sqrt(7)t)+c_{2}sin(sqrt(7)t))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2x)/(dt^2)+2(dx)/(dt)+8x=0

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 8 x = 0

x = e^{- t} (c_{1} cos (7 t) + c_{2} sin (7 t))

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 8 x = 0

Solve linear ODE:

x = e^{- t} (c_{1} cos (7 t) + c_{2} sin (7 t))

x = e^{- t} (c_{1} cos (7 t) + c_{2} sin (7 t))

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 8 x = 0

x \cdot y^{^{''}} + 2 x \cdot y^{^{'}} + x \cdot y = 0

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

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

y^{^{'''}} - 11 y^{^{''}} + 24 y^{^{'}} + 36 y = 0

What is the solution for (d^2x)/(dt^2)+2(dx)/(dt)+8x=0 ?
The solution for (d^2x)/(dt^2)+2(dx)/(dt)+8x=0 is x=e^{-t}(c_{1}cos(sqrt(7)t)+c_{2}sin(sqrt(7)t))