What is the solution for y^{''}+18y^'+81y=t^{-2}e^{-9t} ?

The solution for y^{''}+18y^'+81y=t^{-2}e^{-9t} is y=c_{1}e^{-9t}+c_{2}te^{-9t}-e^{-9t}ln(t)-e^{-9t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+18y^'+81y=t^{-2}e^{-9t}

y^{^{''}} + 18 y^{^{'}} + 81 y = t^{- 2} e^{- 9 t}

y = c_{1} e^{- 9 t} + c_{2} t e^{- 9 t} - e^{- 9 t} ln (t) - e^{- 9 t}

Solution steps

y^{''} (t) + 18 y^{'} (t) + 81 y = t^{- 2} e^{- 9 t}

Solve linear ODE:

y = c_{1} e^{- 9 t} + c_{2} t e^{- 9 t} - e^{- 9 t} ln (t) - e^{- 9 t}

y = c_{1} e^{- 9 t} + c_{2} t e^{- 9 t} - e^{- 9 t} ln (t) - e^{- 9 t}

x \to - 5 lim (\frac{x ^{2} - 2}{x + 5})

\int \frac{1}{( x + 1 ) ( x ^{2} + 4 )} d x

- 6 y^{^{''}} + 54 y^{^{'}} = 0, y (2) = 1, y^{^{'}} (- 1) = 1

\int_{1}^{2} 2 x (1 - \frac{1}{x ^{2}}) d x

What is the solution for y^{''}+18y^'+81y=t^{-2}e^{-9t} ?
The solution for y^{''}+18y^'+81y=t^{-2}e^{-9t} is y=c_{1}e^{-9t}+c_{2}te^{-9t}-e^{-9t}ln(t)-e^{-9t}