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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{x ^{2}}{1 + 2 x}

(6 y + 2 x - 7) d x + (8 y + 6 x - 1) d y = 0

x \to + 3 lim (\frac{6 x}{x - 3})

e^{x^{2}}

\int 2 sin (5 x) d x

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