What is the solution for 9((d^2y)/(dx^2))+12((dy)/(dx))+4y=0 ?

The solution for 9((d^2y)/(dx^2))+12((dy)/(dx))+4y=0 is y=c_{1}e^{-(2x)/3}+c_{2}e^{-(2x)/3}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

9((d^2y)/(dx^2))+12((dy)/(dx))+4y=0

9 (\frac{d ^{2} y}{d x ^{2}}) + 12 (\frac{d y}{d x}) + 4 y = 0

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

Solution steps

9 (\frac{d ^{2} y}{d x ^{2}}) + 12 (\frac{d y}{d x}) + 4 y = 0

Solve linear ODE:

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

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

2 y^{^{''}} + 4 y^{^{'}} + k y = 0

\frac{d ^{2} y}{d x ^{2}} (4) + \frac{d y}{d x} (5) + y = 0

y^{^{''}} + 4 y^{^{'}} - 32 y = 0, y (0) = - 3

x^{^{'''}} + x^{^{''}} - 72 x^{^{'}} = 0

y^{^{''''}} = 256 y

What is the solution for 9((d^2y)/(dx^2))+12((dy)/(dx))+4y=0 ?
The solution for 9((d^2y)/(dx^2))+12((dy)/(dx))+4y=0 is y=c_{1}e^{-(2x)/3}+c_{2}e^{-(2x)/3}x