What is the solution for y^{''}+8y^'+15y=3e^{-3t} ?

The solution for y^{''}+8y^'+15y=3e^{-3t} is y=c_{1}e^{-3t}+c_{2}e^{-5t}+(3e^{-3t}t)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+8y^'+15y=3e^{-3t}

y^{^{''}} + 8 y^{^{'}} + 15 y = 3 e^{- 3 t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 5 t} + \frac{3 e ^{- 3 t} t}{2}

Solution steps

y^{''} (t) + 8 y^{'} (t) + 15 y = 3 e^{- 3 t}

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 5 t} + \frac{3 e ^{- 3 t} t}{2}

y = c_{1} e^{- 3 t} + c_{2} e^{- 5 t} + \frac{3 e ^{- 3 t} t}{2}

y^{^{''}} - y^{^{'}} - 12 y = - 5 e^{3 x}

y^{^{''}} + 5 y^{^{'}} + 4 = 0

\frac{d ^{2} y}{d x ^{2}} + y = 3 cos (2 x)

y^{^{''}} + 2 y^{^{'}} = 3 + sin (t)

y^{^{''}} - 2 y + 10 y = e^{x} cos (3 x)

What is the solution for y^{''}+8y^'+15y=3e^{-3t} ?
The solution for y^{''}+8y^'+15y=3e^{-3t} is y=c_{1}e^{-3t}+c_{2}e^{-5t}+(3e^{-3t}t)/2