What is the solution for 2y^{''}-y^'-y=3e^x+2e^{-x} ?

The solution for 2y^{''}-y^'-y=3e^x+2e^{-x} is y=c_{1}e^x+c_{2}e^{-x/2}+e^xx+e^{-x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2y^{''}-y^'-y=3e^x+2e^{-x}

2 y^{^{''}} - y^{^{'}} - y = 3 e^{x} + 2 e^{- x}

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

Solution steps

2 y^{''} (x) - y^{'} (x) - y = 3 e^{x} + 2 e^{- x}

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + y = t^{(- 1)} e^{(- t)}

y^{^{''}} - y^{^{'}} - 6 y = 2 e^{3 t}, y (0) = 3, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} = 5 x

(D^{2} + 2 D - 3) y = cos (2 x)

y^{^{''}} - 8 y^{^{'}} = 6 e^{2 x} - 6 x^{2} - 9 x - 14

What is the solution for 2y^{''}-y^'-y=3e^x+2e^{-x} ?
The solution for 2y^{''}-y^'-y=3e^x+2e^{-x} is y=c_{1}e^x+c_{2}e^{-x/2}+e^xx+e^{-x}