What is the solution for D^2(D+2)y=2+e^{(-t)/2} ?

The solution for D^2(D+2)y=2+e^{(-t)/2} is y=c_{1}e^{-2t}+c_{2}+c_{3}t+(t^2)/2+8/3 e^{-t/2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

D^2(D+2)y=2+e^{(-t)/2}

D^{2} (D + 2) y = 2 + e^{\frac{- t}{2}}

y = c_{1} e^{- 2 t} + c_{2} + c_{3} t + \frac{t ^{2}}{2} + \frac{8}{3} e^{- \frac{t}{2}}

Solution steps

D^{2} (D + 2) y = 2 + e^{\frac{- t}{2}}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} + c_{3} t + \frac{t ^{2}}{2} + \frac{8}{3} e^{- \frac{t}{2}}

y = c_{1} e^{- 2 t} + c_{2} + c_{3} t + \frac{t ^{2}}{2} + \frac{8}{3} e^{- \frac{t}{2}}

x^{^{''}} + x^{^{'}} = 2 t + 1

y^{^{''''}} + 2 y^{^{''}} + y = 3 t + 8

y^{^{''}} - 9 y^{^{'}} + 18 = 0

y^{^{''}} - 2 y^{^{'}} + y = \frac{6 e ^{x}}{1 + x ^{2}}

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

What is the solution for D^2(D+2)y=2+e^{(-t)/2} ?
The solution for D^2(D+2)y=2+e^{(-t)/2} is y=c_{1}e^{-2t}+c_{2}+c_{3}t+(t^2)/2+8/3 e^{-t/2}