What is the solution for y^{''}+5y^'=0,y(0)=9,y^'(0)=-20 ?

The solution for y^{''}+5y^'=0,y(0)=9,y^'(0)=-20 is y=4e^{-5t}+5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}+5y^'=0,y(0)=9,y^'(0)=-20

y^{^{''}} + 5 y^{^{'}} = 0, y (0) = 9, y^{^{'}} (0) = - 20

y = 4 e^{- 5 t} + 5

Solution steps

y^{''} (t) + 5 y^{'} (t) = 0

Solve linear ODE:

y = 4 e^{- 5 t} + 5

y = 4 e^{- 5 t} + 5

\frac{d ^{2} x}{d t ^{2}} + 6 \cdot \frac{d x}{d t} + 3 \cdot x = 0, x (0) = 0

4 (\frac{d ^{2} y}{d x ^{2}}) + 4 (\frac{d y}{d x}) + y = 0

2500 y^{^{''}} + 81 y = 0

y^{^{''}} + 5 y^{^{'}} - 24 y = 0, y (0) = x, y^{^{'}} (0) = 56

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

What is the solution for y^{''}+5y^'=0,y(0)=9,y^'(0)=-20 ?
The solution for y^{''}+5y^'=0,y(0)=9,y^'(0)=-20 is y=4e^{-5t}+5