What is the solution for y^{''}+2y^'+y=5y-y^{''}+2y^'-y ?

The solution for y^{''}+2y^'+y=5y-y^{''}+2y^'-y is y=c_{1}e^{sqrt(3/2)t}+c_{2}e^{-sqrt(3/2)t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}+2y^'+y=5y-y^{''}+2y^'-y

y^{^{''}} + 2 y^{^{'}} + y = 5 y - y^{^{''}} + 2 y^{^{'}} - y

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

Solution steps

y^{''} (t) + 2 y^{'} (t) + y = 5 y - y^{''} (t) + 2 y^{'} (t) - y

Solve linear ODE:

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

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

What is the solution for y^{''}+2y^'+y=5y-y^{''}+2y^'-y ?
The solution for y^{''}+2y^'+y=5y-y^{''}+2y^'-y is y=c_{1}e^{sqrt(3/2)t}+c_{2}e^{-sqrt(3/2)t}