What is the solution for 2y^{''}+y^'-y=1,y^'(0)=0 ?

The solution for 2y^{''}+y^'-y=1,y^'(0)=0 is y=2c_{2}e^{t/2}+c_{2}e^{-t}-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

2 y^{''} (t) + y^{'} (t) - y = 1

Solve linear ODE:

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

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

What is the solution for 2y^{''}+y^'-y=1,y^'(0)=0 ?
The solution for 2y^{''}+y^'-y=1,y^'(0)=0 is y=2c_{2}e^{t/2}+c_{2}e^{-t}-1