What is the solution for y^{''}-2y^'-3y=4e^x-3 ?

The solution for y^{''}-2y^'-3y=4e^x-3 is y=c_{1}e^{3x}+c_{2}e^{-x}-e^x+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-2y^'-3y=4e^x-3

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 3

y = c_{1} e^{3 x} + c_{2} e^{- x} - e^{x} + 1

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 4 e^{x} - 3

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} - e^{x} + 1

y = c_{1} e^{3 x} + c_{2} e^{- x} - e^{x} + 1

What is the solution for y^{''}-2y^'-3y=4e^x-3 ?
The solution for y^{''}-2y^'-3y=4e^x-3 is y=c_{1}e^{3x}+c_{2}e^{-x}-e^x+1