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

The solution for y^{''}+2y^'+y=xe^{-x}+4 is y=c_{1}e^{-x}+c_{2}xe^{-x}+(e^{-x}x^3)/6+4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+2y^'+y=xe^{-x}+4

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

y = c_{1} e^{- x} + c_{2} x e^{- x} + \frac{e ^{- x} x ^{3}}{6} + 4

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} + \frac{e ^{- x} x ^{3}}{6} + 4

y = c_{1} e^{- x} + c_{2} x e^{- x} + \frac{e ^{- x} x ^{3}}{6} + 4

y^{^{''}} + 2 y = - 8 x sin (3 x)

y^{^{''}} - 14 y^{^{'}} + 49 y = 10 e^{7 x}

y^{^{''}} + y^{^{'}} - 12 y = sin (t), y (0) = 1, y^{^{'}} (0) = 1

y, (d^{2} + 5 d + 6) y = (d + 1) 6 t^{2}

y^{^{''}} - 6 y^{^{'}} + 10 y = 10 x^{2} + 8 x

What is the solution for y^{''}+2y^'+y=xe^{-x}+4 ?
The solution for y^{''}+2y^'+y=xe^{-x}+4 is y=c_{1}e^{-x}+c_{2}xe^{-x}+(e^{-x}x^3)/6+4