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

The solution for y^{''}+6y^'+9y=e^x is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+1/16 e^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{1}{16} e^{x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{1}{16} e^{x}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{1}{16} e^{x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 6 x e^{- 3 x} + 27 x + 27

y^{^{''}} + 3 y^{^{'}} - 10 y = - 42 t + 20 t^{2}

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

4 q^{^{''}} + 8 q^{^{'}} + 80 q = 88

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

What is the solution for y^{''}+6y^'+9y=e^x ?
The solution for y^{''}+6y^'+9y=e^x is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+1/16 e^x