What is the solution for (d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t} ?

The solution for (d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t} is x=c_{1}e^{-t}+c_{2}e^{-6t}+e^{-t}t

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t}

\frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 6 x = 5 e^{- t}

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + e^{- t} t

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 6 x = 5 e^{- t}

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + e^{- t} t

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + e^{- t} t

What is the solution for (d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t} ?
The solution for (d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t} is x=c_{1}e^{-t}+c_{2}e^{-6t}+e^{-t}t