What is the solution for y^{''}+y^'-2y=x^2 ?

The solution for y^{''}+y^'-2y=x^2 is y=c_{1}e^x+c_{2}e^{-2x}-(x^2)/2-x/2-3/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{3}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{3}{4}

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{3}{4}

What is the solution for y^{''}+y^'-2y=x^2 ?
The solution for y^{''}+y^'-2y=x^2 is y=c_{1}e^x+c_{2}e^{-2x}-(x^2)/2-x/2-3/4