What is the solution for y^{''}+y^'-12y=-32t+24t^2 ?

The solution for y^{''}+y^'-12y=-32t+24t^2 is y=c_{1}e^{3t}+c_{2}e^{-4t}-2t^2+(7t)/3-5/36

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}+y^'-12y=-32t+24t^2

y^{^{''}} + y^{^{'}} - 12 y = - 32 t + 24 t^{2}

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - 2 t^{2} + \frac{7 t}{3} - \frac{5}{36}

Solution steps

y^{''} (t) + y^{'} (t) - 12 y = - 32 t + 24 t^{2}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - 2 t^{2} + \frac{7 t}{3} - \frac{5}{36}

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - 2 t^{2} + \frac{7 t}{3} - \frac{5}{36}

What is the solution for y^{''}+y^'-12y=-32t+24t^2 ?
The solution for y^{''}+y^'-12y=-32t+24t^2 is y=c_{1}e^{3t}+c_{2}e^{-4t}-2t^2+(7t)/3-5/36