en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+6y^'+45y=6,y(0)=5,y^'(0)=9

Solution

y^{^{''}} + 6 y^{^{'}} + 45 y = 6, y (0) = 5, y^{^{'}} (0) = 9

Solution

y = e^{- 3 t} (\frac{73}{15} cos (6 t) + \frac{59}{15} sin (6 t)) + \frac{2}{15}

Solution steps

y^{''} (t) + 6 y^{'} (t) + 45 y = 6

Solve linear ODE:

y = e^{- 3 t} (\frac{73}{15} cos (6 t) + \frac{59}{15} sin (6 t)) + \frac{2}{15}

y = e^{- 3 t} (\frac{73}{15} cos (6 t) + \frac{59}{15} sin (6 t)) + \frac{2}{15}

Graph

Popular Examples

y^{''}+5y^'+4y=3e^{-5x},y(0)=5,y^'(0)=3

y^{^{''}} + 5 y^{^{'}} + 4 y = 3 e^{- 5 x}, y (0) = 5, y^{^{'}} (0) = 3

y^{''}-4y^'+3y=5e^{3t}

y^{^{''}} - 4 y^{^{'}} + 3 y = 5 e^{3 t}

y^{'''}-y^{''}-9y^'+9y=4-e^x+e^{3x}

y^{^{'''}} - y^{^{''}} - 9 y^{^{'}} + 9 y = 4 - e^{x} + e^{3 x}

y^{''}+36y=6cos(6x)+9sin(6x)

y^{^{''}} + 36 y = 6 cos (6 x) + 9 sin (6 x)

y^{''}+8y^'+16y=8sin(2t)

y^{^{''}} + 8 y^{^{'}} + 16 y = 8 sin (2 t)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+6y^'+45y=6,y(0)=5,y^'(0)=9 ?
The solution for y^{''}+6y^'+45y=6,y(0)=5,y^'(0)=9 is y=e^{-3t}(73/15 cos(6t)+59/15 sin(6t))+2/15