What is the solution for y^{''}-6y^'-16y=0,y(0)=2,y^'(0)=4 ?

The solution for y^{''}-6y^'-16y=0,y(0)=2,y^'(0)=4 is y=(2-6/5)e^{8t}+6/5 e^{-2t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-6y^'-16y=0,y(0)=2,y^'(0)=4

y^{^{''}} - 6 y^{^{'}} - 16 y = 0, y (0) = 2, y^{^{'}} (0) = 4

y = (2 - \frac{6}{5}) e^{8 t} + \frac{6}{5} e^{- 2 t}

Solution steps

y^{''} (t) - 6 y^{'} (t) - 16 y = 0

Solve linear ODE:

y = (2 - \frac{6}{5}) e^{8 t} + \frac{6}{5} e^{- 2 t}

y = (2 - \frac{6}{5}) e^{8 t} + \frac{6}{5} e^{- 2 t}

4 y^{^{''}} + 4 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = 8

y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 2, y^{^{'}} (0) = - 6

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

y^{^{''}} - (8) y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 73

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 0, y^{^{'}} (0) = 1

What is the solution for y^{''}-6y^'-16y=0,y(0)=2,y^'(0)=4 ?
The solution for y^{''}-6y^'-16y=0,y(0)=2,y^'(0)=4 is y=(2-6/5)e^{8t}+6/5 e^{-2t}