What is the solution for y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-1 ?

The solution for y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-1 is y=(1-5/7)e^{4t}+5/7 e^{-3t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-1

y^{^{''}} - y^{^{'}} - 12 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

y = (1 - \frac{5}{7}) e^{4 t} + \frac{5}{7} e^{- 3 t}

Solution steps

y^{''} (t) - y^{'} (t) - 12 y = 0

Solve linear ODE:

y = (1 - \frac{5}{7}) e^{4 t} + \frac{5}{7} e^{- 3 t}

y = (1 - \frac{5}{7}) e^{4 t} + \frac{5}{7} e^{- 3 t}

24 y^{^{''}} + 7 y^{^{'}} - 5 y = 0

2 y^{^{''}} + 12 y^{^{'}} + 18 y = 0

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y^{^{'}} (0) = - 2

x^{^{''}} + 42 x^{^{'}} + 8 x = 0

y^{^{''}} + 2 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-1 ?
The solution for y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-1 is y=(1-5/7)e^{4t}+5/7 e^{-3t}