What is the solution for y^{''}-9y=0,y(0)=36,y^'(0)=-36 ?

The solution for y^{''}-9y=0,y(0)=36,y^'(0)=-36 is y=12e^{3t}+24e^{-3t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-9y=0,y(0)=36,y^'(0)=-36

y^{^{''}} - 9 y = 0, y (0) = 36, y^{^{'}} (0) = - 36

y = 12 e^{3 t} + 24 e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = 12 e^{3 t} + 24 e^{- 3 t}

y = 12 e^{3 t} + 24 e^{- 3 t}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + 6 y = 0

3 y^{^{'''}} + 4 y^{^{''}} = 0

100 y^{^{''}} + 40 y^{^{'}} - 45 y = 0

2 y^{^{''}} + 6 y^{^{'}} - \frac{9 y}{2} = 0

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

What is the solution for y^{''}-9y=0,y(0)=36,y^'(0)=-36 ?
The solution for y^{''}-9y=0,y(0)=36,y^'(0)=-36 is y=12e^{3t}+24e^{-3t}