What is the solution for y^{''}+2y^'-3y=8xe^x ?

The solution for y^{''}+2y^'-3y=8xe^x is y=c_{1}e^x+c_{2}e^{-3x}+e^xx^2-(e^xx)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+2y^'-3y=8xe^x

y^{^{''}} + 2 y^{^{'}} - 3 y = 8 x e^{x}

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y = 5 t^{2} - 3, y (0) = 0, y^{^{'}} (0) = - 6

10 y^{^{''}} + 1000 y = 140 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = 2 t^{2} - 4, y (0) = 0, y^{^{'}} (0) = - 4

y^{^{''}} + 3 y^{^{'}} + 4 y = 2 sin (3 t)

y^{^{''}} + y^{^{'}} = 2 x + x

What is the solution for y^{''}+2y^'-3y=8xe^x ?
The solution for y^{''}+2y^'-3y=8xe^x is y=c_{1}e^x+c_{2}e^{-3x}+e^xx^2-(e^xx)/2