What is the solution for y^{''}-16y=48t-24e^{-4t},y(0)=0,y^'(0)=16 ?

The solution for y^{''}-16y=48t-24e^{-4t},y(0)=0,y^'(0)=16 is y=2e^{4t}-2e^{-4t}-3t+3e^{-4t}t

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-16y=48t-24e^{-4t},y(0)=0,y^'(0)=16

y^{^{''}} - 16 y = 48 t - 24 e^{- 4 t}, y (0) = 0, y^{^{'}} (0) = 16

y = 2 e^{4 t} - 2 e^{- 4 t} - 3 t + 3 e^{- 4 t} t

Solution steps

y^{''} (t) - 16 y = 48 t - 24 e^{- 4 t}

Solve linear ODE:

y = 2 e^{4 t} - 2 e^{- 4 t} - 3 t + 3 e^{- 4 t} t

y = 2 e^{4 t} - 2 e^{- 4 t} - 3 t + 3 e^{- 4 t} t

What is the solution for y^{''}-16y=48t-24e^{-4t},y(0)=0,y^'(0)=16 ?
The solution for y^{''}-16y=48t-24e^{-4t},y(0)=0,y^'(0)=16 is y=2e^{4t}-2e^{-4t}-3t+3e^{-4t}t