What is the solution for (4+8x)y^{''}-8y+(4-8x)y=0 ?

The solution for (4+8x)y^{''}-8y+(4-8x)y=0 is y=c_{1}e^x+c_{2}e^{-x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(4+8x)y^{''}-8y+(4-8x)y=0

(4 + 8 x) y^{^{''}} - 8 y + (4 - 8 x) y = 0

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

Solution steps

(4 + 8 x) y^{''} (x) - 8 y + (4 - 8 x) y = 0

Solve linear ODE:

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

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

y^{^{''}} - 4 y - 4 y = 0

y^{^{''''}} + y^{^{'}} = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (0) = 0

(2 \cdot y^{^{''}}) - (3 \cdot y^{^{'}}) - (2 \cdot y) = 0

y^{^{''}} + 20.02 y = 0, y (0) = 0, y^{^{'}} (0) = - 2

What is the solution for (4+8x)y^{''}-8y+(4-8x)y=0 ?
The solution for (4+8x)y^{''}-8y+(4-8x)y=0 is y=c_{1}e^x+c_{2}e^{-x}