What is the solution for y^{''}-2y^'-3y=6,y(0)=9,y^'(0)=27 ?

The solution for y^{''}-2y^'-3y=6,y(0)=9,y^'(0)=27 is y=(-3/2+11)e^{3t}+3/2 e^{-t}-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-2y^'-3y=6,y(0)=9,y^'(0)=27

y^{^{''}} - 2 y^{^{'}} - 3 y = 6, y (0) = 9, y^{^{'}} (0) = 27

y = (- \frac{3}{2} + 11) e^{3 t} + \frac{3}{2} e^{- t} - 2

Solution steps

y^{''} (t) - 2 y^{'} (t) - 3 y = 6

Solve linear ODE:

y = (- \frac{3}{2} + 11) e^{3 t} + \frac{3}{2} e^{- t} - 2

y = (- \frac{3}{2} + 11) e^{3 t} + \frac{3}{2} e^{- t} - 2

y^{^{''}} + y^{^{'}} - 6 y = 3 x + 2

y^{^{''}} - 2 y^{^{'}} + 2 y = 2 x + 2

y^{^{''}} - 2 y^{^{'}} - 2 y = - 1 + 5 x^{2} + x^{3}

y^{^{''}} - 8 y^{^{'}} + 15 y = t e^{3 t}

y^{^{'''}} - 3 y^{^{''}} + y^{^{'}} - 3 y = e^{x} + 2

What is the solution for y^{''}-2y^'-3y=6,y(0)=9,y^'(0)=27 ?
The solution for y^{''}-2y^'-3y=6,y(0)=9,y^'(0)=27 is y=(-3/2+11)e^{3t}+3/2 e^{-t}-2