What is the solution for 4y^{''}+36y^'+81y=0 ?

The solution for 4y^{''}+36y^'+81y=0 is y=c_{1}e^{-(9t)/2}+c_{2}e^{-(9t)/2}t

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

4y^{''}+36y^'+81y=0

4 y^{^{''}} + 36 y^{^{'}} + 81 y = 0

y = c_{1} e^{- \frac{9 t}{2}} + c_{2} e^{- \frac{9 t}{2}} t

Solution steps

4 y^{''} (t) + 36 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{9 t}{2}} + c_{2} e^{- \frac{9 t}{2}} t

y = c_{1} e^{- \frac{9 t}{2}} + c_{2} e^{- \frac{9 t}{2}} t

t an g e n t - 3 x^{2} + 6 x - 2

f^{^{'}} (x) = sec (2 x) tan (2 x)

\frac{d y}{d x} = 2 y (3 - x)

\int \frac{x ^{2}}{x ^{2} - 3 x + 2} d x

d er i v a t i v e f (x) = 12

What is the solution for 4y^{''}+36y^'+81y=0 ?
The solution for 4y^{''}+36y^'+81y=0 is y=c_{1}e^{-(9t)/2}+c_{2}e^{-(9t)/2}t