What is the solution for (d^2y)/(dt^2)+8(dy)/(dt)-20y=5e^{-3t} ?

The solution for (d^2y)/(dt^2)+8(dy)/(dt)-20y=5e^{-3t} is y=c_{1}e^{2t}+c_{2}e^{-10t}-1/7 e^{-3t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dt^2)+8(dy)/(dt)-20y=5e^{-3t}

\frac{d ^{2} y}{d t ^{2}} + 8 \frac{d y}{d t} - 20 y = 5 e^{- 3 t}

y = c_{1} e^{2 t} + c_{2} e^{- 10 t} - \frac{1}{7} e^{- 3 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 8 \frac{d y}{d t} - 20 y = 5 e^{- 3 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 10 t} - \frac{1}{7} e^{- 3 t}

y = c_{1} e^{2 t} + c_{2} e^{- 10 t} - \frac{1}{7} e^{- 3 t}

y^{^{''}} + y^{^{'}} + 4 = - 20 x

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 3

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 2

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 15 = 0

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{2} + 3 x

What is the solution for (d^2y)/(dt^2)+8(dy)/(dt)-20y=5e^{-3t} ?
The solution for (d^2y)/(dt^2)+8(dy)/(dt)-20y=5e^{-3t} is y=c_{1}e^{2t}+c_{2}e^{-10t}-1/7 e^{-3t}