What is the solution for q^{''}+3q^'+2q=e^{-t}+e^{-2t} ?

The solution for q^{''}+3q^'+2q=e^{-t}+e^{-2t} is q(t)=c_{1}e^{-t}+c_{2}e^{-2t}+e^{-t}t-e^{-2t}t

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

q^{''}+3q^'+2q=e^{-t}+e^{-2t}

q^{^{''}} + 3 q^{^{'}} + 2 q = e^{- t} + e^{- 2 t}

q (t) = c_{1} e^{- t} + c_{2} e^{- 2 t} + e^{- t} t - e^{- 2 t} t

Solution steps

q^{''} (t) + 3 q^{'} (t) + 2 q (t) = e^{- t} + e^{- 2 t}

Solve linear ODE:

q (t) = c_{1} e^{- t} + c_{2} e^{- 2 t} + e^{- t} t - e^{- 2 t} t

q (t) = c_{1} e^{- t} + c_{2} e^{- 2 t} + e^{- t} t - e^{- 2 t} t

What is the solution for q^{''}+3q^'+2q=e^{-t}+e^{-2t} ?
The solution for q^{''}+3q^'+2q=e^{-t}+e^{-2t} is q(t)=c_{1}e^{-t}+c_{2}e^{-2t}+e^{-t}t-e^{-2t}t