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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 3 y = cos (3 x)

y^{^{''}} - 4 y = 4 t - 8 e^{- 2 t}

y^{^{''}} + y^{^{'}} = cos (3 t), y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 8 y^{^{'}} + 16 y = \frac{3 e ^{- 4 x}}{x ^{4}}

y^{^{''}} - 2 y^{^{'}} - 3 y = 4, y^{^{'}} (0) = - 1

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