What is the solution for y^{''}-6y^'+9y=0,y(0)=1,y(1)=0 ?

The solution for y^{''}-6y^'+9y=0,y(0)=1,y(1)=0 is y=e^{3t}-e^{3t}t

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-6y^'+9y=0,y(0)=1,y(1)=0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 1, y (1) = 0

y = e^{3 t} - e^{3 t} t

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = e^{3 t} - e^{3 t} t

y = e^{3 t} - e^{3 t} t

\frac{d ^{2} x}{d t ^{2}} + 81 x = 0

\frac{1}{4} y^{^{''}} + y^{^{'}} + 4 y = 0

y^{^{'''}} + 5 y^{^{''}} + 3 y^{^{'}} - 9 y = 0

y^{^{'''}} + 2 y^{^{'}} - 3 y = 0

15 y^{^{''''}} + 128 y^{^{''}} + 25 y = 0

What is the solution for y^{''}-6y^'+9y=0,y(0)=1,y(1)=0 ?
The solution for y^{''}-6y^'+9y=0,y(0)=1,y(1)=0 is y=e^{3t}-e^{3t}t