What is the solution for 36y^{''}-108y^'+81y=0,y(0)=7,y^'(0)=1 ?

The solution for 36y^{''}-108y^'+81y=0,y(0)=7,y^'(0)=1 is y=7e^{(3t)/2}-(19e^{(3t)/2}t)/(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

36y^{''}-108y^'+81y=0,y(0)=7,y^'(0)=1

36 y^{^{''}} - 108 y^{^{'}} + 81 y = 0, y (0) = 7, y^{^{'}} (0) = 1

y = 7 e^{\frac{3 t}{2}} - \frac{19 e ^{\frac{3 t}{2}} t}{2}

Solution steps

36 y^{''} (t) - 108 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = 7 e^{\frac{3 t}{2}} - \frac{19 e ^{\frac{3 t}{2}} t}{2}

y = 7 e^{\frac{3 t}{2}} - \frac{19 e ^{\frac{3 t}{2}} t}{2}

What is the solution for 36y^{''}-108y^'+81y=0,y(0)=7,y^'(0)=1 ?
The solution for 36y^{''}-108y^'+81y=0,y(0)=7,y^'(0)=1 is y=7e^{(3t)/2}-(19e^{(3t)/2}t)/(2)