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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

y^{^{''}} + 3 \cdot y^{^{'}} + 2 y = sin (e^{x})

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - e^{- 2 x} sin (e^{x})

Solution steps

y^{''} (x) + 3 \cdot y^{'} (x) + 2 y = sin (e^{x})

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - e^{- 2 x} sin (e^{x})

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - e^{- 2 x} sin (e^{x})

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

y^{^{'''}} + 12 y^{^{''}} - 256 y = e^{- 8 x}

8 y^{^{''}} + 3 y^{^{'}} = 12 x

y^{^{''}} + y^{^{'}} - 6 y = e^{2 t}

y^{^{''}} - 4 y^{^{'}} + 5 y = (x + 1)^{3}

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