What is the solution for y^{''}+4y^'+3y=6x^2+x+9 ?

The solution for y^{''}+4y^'+3y=6x^2+x+9 is y=c_{1}e^{-x}+c_{2}e^{-3x}+2x^2-5x+25/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}+4y^'+3y=6x^2+x+9

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 x^{2} + x + 9

y = c_{1} e^{- x} + c_{2} e^{- 3 x} + 2 x^{2} - 5 x + \frac{25}{3}

Solution steps

y^{''} (x) + 4 y^{'} (x) + 3 y = 6 x^{2} + x + 9

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 3 x} + 2 x^{2} - 5 x + \frac{25}{3}

y = c_{1} e^{- x} + c_{2} e^{- 3 x} + 2 x^{2} - 5 x + \frac{25}{3}

What is the solution for y^{''}+4y^'+3y=6x^2+x+9 ?
The solution for y^{''}+4y^'+3y=6x^2+x+9 is y=c_{1}e^{-x}+c_{2}e^{-3x}+2x^2-5x+25/3