What is the solution for y^{''}-y^'-12y=2t^6e^{-3t} ?

The solution for y^{''}-y^'-12y=2t^6e^{-3t} is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-y^'-12y=2t^6e^{-3t}

y^{^{''}} - y^{^{'}} - 12 y = 2 t^{6} e^{- 3 t}

y = c_{1} e^{4 t} + c_{2} e^{- 3 t} - \frac{2 e ^{- 3 t} t ^{7}}{49} - \frac{2 e ^{- 3 t} t ^{6}}{49} - \frac{12 e ^{- 3 t} t ^{5}}{343} - \frac{60 e ^{- 3 t} t ^{4}}{2401} - \frac{240 e ^{- 3 t} t ^{3}}{16807} - \frac{720 e ^{- 3 t} t ^{2}}{117649} - \frac{1440 e ^{- 3 t} t}{823543}

Solution steps

y^{''} (t) - y^{'} (t) - 12 y = 2 t^{6} e^{- 3 t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 3 t} - \frac{2 e ^{- 3 t} t ^{7}}{49} - \frac{2 e ^{- 3 t} t ^{6}}{49} - \frac{12 e ^{- 3 t} t ^{5}}{343} - \frac{60 e ^{- 3 t} t ^{4}}{2401} - \frac{240 e ^{- 3 t} t ^{3}}{16807} - \frac{720 e ^{- 3 t} t ^{2}}{117649} - \frac{1440 e ^{- 3 t} t}{823543}

y = c_{1} e^{4 t} + c_{2} e^{- 3 t} - \frac{2 e ^{- 3 t} t ^{7}}{49} - \frac{2 e ^{- 3 t} t ^{6}}{49} - \frac{12 e ^{- 3 t} t ^{5}}{343} - \frac{60 e ^{- 3 t} t ^{4}}{2401} - \frac{240 e ^{- 3 t} t ^{3}}{16807} - \frac{720 e ^{- 3 t} t ^{2}}{117649} - \frac{1440 e ^{- 3 t} t}{823543}

What is the solution for y^{''}-y^'-12y=2t^6e^{-3t} ?
The solution for y^{''}-y^'-12y=2t^6e^{-3t} is