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

The solution for y^{''}+3y^'+2y=e^{-x}(3-4x) is y=c_{1}e^{-x}+c_{2}e^{-2x}-2x^2e^{-x}+7xe^{-x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - 2 x^{2} e^{- x} + 7 x e^{- x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - 2 x^{2} e^{- x} + 7 x e^{- x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - 2 x^{2} e^{- x} + 7 x e^{- x}

y^{^{''}} - 16 y^{^{'}} = 2 e^{4 x}

y^{^{'''}} + 4 y^{^{'}} = t^{2} + 2 t

y^{^{''}} - y = sin (t), y (0) = 1, y^{^{'}} (0) = 1

4 y^{^{''}} + 8 y^{^{'}} + 5 y = e^{- x} sec (\frac{x}{2})

y^{^{''}} + 2 y^{^{'}} = 24 x + e^{- 2 x}

What is the solution for y^{''}+3y^'+2y=e^{-x}(3-4x) ?
The solution for y^{''}+3y^'+2y=e^{-x}(3-4x) is y=c_{1}e^{-x}+c_{2}e^{-2x}-2x^2e^{-x}+7xe^{-x}