What is the solution for y^{''}+5y^'+6y=18t^2 ?

The solution for y^{''}+5y^'+6y=18t^2 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+3t^2-5t+19/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+5y^'+6y=18t^2

y^{^{''}} + 5 y^{^{'}} + 6 y = 18 t^{2}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + 3 t^{2} - 5 t + \frac{19}{6}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 18 t^{2}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + 3 t^{2} - 5 t + \frac{19}{6}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + 3 t^{2} - 5 t + \frac{19}{6}

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{t}, y (0) = 1, y^{^{'}} (0) = - 6

y^{^{''}} + 2 y^{^{'}} + 4 y = 111 e^{2 t} cos (3 t)

y^{^{''}} + 4 y = \frac{1}{cos ( 2 x )}

2 y^{^{''}} + y^{^{'}} - y = x + 1, y (0) = 1, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} = x + sin (x)

What is the solution for y^{''}+5y^'+6y=18t^2 ?
The solution for y^{''}+5y^'+6y=18t^2 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+3t^2-5t+19/6