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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}=2y-x

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - y \cdot a + g = 0

y^{^{'''}} - 11 y^{^{''}} + 28 y^{^{'}} = 36 e^{x}, y^{^{'}} (0) = 26

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

y^{^{''}} - 10 y^{^{'}} + 24 y = 150 e^{t}

y^{^{''}} - 2 y^{^{'}} = 12 x + 10

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