What is the solution for y^{''}+y^'-12y=0,y(0)=4,y^'(0)=-9 ?

The solution for y^{''}+y^'-12y=0,y(0)=4,y^'(0)=-9 is y=e^{3t}+3e^{-4t}

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)=4,y^'(0)=-9

y^{^{''}} + y^{^{'}} - 12 y = 0, y (0) = 4, y^{^{'}} (0) = - 9

y = e^{3 t} + 3 e^{- 4 t}

Solution steps

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

Solve linear ODE:

y = e^{3 t} + 3 e^{- 4 t}

y = e^{3 t} + 3 e^{- 4 t}

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

\frac{d ^{2} x}{d t ^{2}} + 10 \frac{d x}{d t} + 25 x = 0

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 9, y^{^{'}} (0) = - 60

y^{^{'''}} - 7 y^{^{''}} + 12 y^{^{'}} = 0

x^{^{''}} + 2 x^{^{'}} - 8 x = 0, x^{^{'}} (0) = 22, x (0) = - 1

What is the solution for y^{''}+y^'-12y=0,y(0)=4,y^'(0)=-9 ?
The solution for y^{''}+y^'-12y=0,y(0)=4,y^'(0)=-9 is y=e^{3t}+3e^{-4t}