What is the solution for y^{''}+6y^'+9y=e^{-3x} ?

The solution for y^{''}+6y^'+9y=e^{-3x} is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+(e^{-3x}x^2)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{''}} - y^{^{'}} - 2 y = 6 x + 5 e^{4 x}

y^{^{''}} - 4 y^{^{'}} - 12 y = e^{- 2 x} + 5 x + 2

y^{^{''}} - 4 y^{^{'}} + 5 y = 24 cos (x)

y^{^{'''}} + 3 y^{^{''}} - 4 = 5 t^{2} + 4

What is the solution for y^{''}+6y^'+9y=e^{-3x} ?
The solution for y^{''}+6y^'+9y=e^{-3x} is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+(e^{-3x}x^2)/2