What is the solution for y^{''}+2y^'-8y=4e^{-3x}-e^{-x} ?

The solution for y^{''}+2y^'-8y=4e^{-3x}-e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-4x}-4/5 e^{-3x}+1/9 e^{-x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+2y^'-8y=4e^{-3x}-e^{-x}

y^{^{''}} + 2 y^{^{'}} - 8 y = 4 e^{- 3 x} - e^{- x}

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} - \frac{4}{5} e^{- 3 x} + \frac{1}{9} e^{- x}

Solution steps

y^{''} (x) + 2 y^{'} (x) - 8 y = 4 e^{- 3 x} - e^{- x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} - \frac{4}{5} e^{- 3 x} + \frac{1}{9} e^{- x}

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} - \frac{4}{5} e^{- 3 x} + \frac{1}{9} e^{- x}

4 \frac{d ^{2} y}{d x ^{2}} - y = x \cdot e^{\frac{x}{2}}

y^{^{''}} + 9 y = 18 t

y^{^{''}} + 4 y = cos (2 t) + sin (t)

4 y^{^{''}} + 4 y^{^{'}} + y = 3 x e^{x}

y^{^{''}} - 6 y + 9 = e^{3 x}

What is the solution for y^{''}+2y^'-8y=4e^{-3x}-e^{-x} ?
The solution for y^{''}+2y^'-8y=4e^{-3x}-e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-4x}-4/5 e^{-3x}+1/9 e^{-x}