What is the solution for y^{'''}-y^{''}-y^'+y=(1+e^{-x}) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{'''}-y^{''}-y^'+y=(1+e^{-x})

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = (1 + e^{- x})

y = c_{1} e^{- x} + c_{2} e^{x} + c_{3} x e^{x} + 1 + \frac{e ^{- x} x}{4}

Solution steps

y^{'''} (x) - y^{''} (x) - y^{'} (x) + y = (1 + e^{- x})

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{x} + c_{3} x e^{x} + 1 + \frac{e ^{- x} x}{4}

y = c_{1} e^{- x} + c_{2} e^{x} + c_{3} x e^{x} + 1 + \frac{e ^{- x} x}{4}

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