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

The solution for 2y^{''}-2y=e^{3x}+e^{-3x} is y=c_{1}e^x+c_{2}e^{-x}+(e^{3x}+e^{-3x})/(16)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{3 x} + e ^{- 3 x}}{16}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{3 x} + e ^{- 3 x}}{16}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{3 x} + e ^{- 3 x}}{16}

What is the solution for 2y^{''}-2y=e^{3x}+e^{-3x} ?
The solution for 2y^{''}-2y=e^{3x}+e^{-3x} is y=c_{1}e^x+c_{2}e^{-x}+(e^{3x}+e^{-3x})/(16)