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

The solution for y^{'''}+y^{''}=3e^{-x}+x is y=c_{1}e^{-x}+c_{2}+c_{3}x+3xe^{-x}+(x^3)/6-(x^2)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{'''}+y^{''}=3e^{-x}+x

y^{^{'''}} + y^{^{''}} = 3 e^{- x} + x

y = c_{1} e^{- x} + c_{2} + c_{3} x + 3 x e^{- x} + \frac{x ^{3}}{6} - \frac{x ^{2}}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} + c_{3} x + 3 x e^{- x} + \frac{x ^{3}}{6} - \frac{x ^{2}}{2}

y = c_{1} e^{- x} + c_{2} + c_{3} x + 3 x e^{- x} + \frac{x ^{3}}{6} - \frac{x ^{2}}{2}

What is the solution for y^{'''}+y^{''}=3e^{-x}+x ?
The solution for y^{'''}+y^{''}=3e^{-x}+x is y=c_{1}e^{-x}+c_{2}+c_{3}x+3xe^{-x}+(x^3)/6-(x^2)/2