What is the solution for 2y^{''}-y^'-y=6e^{-x/2} ?

The solution for 2y^{''}-y^'-y=6e^{-x/2} is y=c_{1}e^x+c_{2}e^{-x/2}-2e^{-x/2}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

2y^{''}-y^'-y=6e^{-x/2}

2 y^{^{''}} - y^{^{'}} - y = 6 e^{- \frac{x}{2}}

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

Solution steps

2 y^{''} (x) - y^{'} (x) - y = 6 e^{- \frac{x}{2}}

Solve linear ODE:

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

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

What is the solution for 2y^{''}-y^'-y=6e^{-x/2} ?
The solution for 2y^{''}-y^'-y=6e^{-x/2} is y=c_{1}e^x+c_{2}e^{-x/2}-2e^{-x/2}x