What is the solution for y^{''}-y^'+1/4 y=9+e^{x/2} ?

The solution for y^{''}-y^'+1/4 y=9+e^{x/2} is y=c_{1}e^{x/2}+c_{2}e^{x/2}x+36+(e^{x/2}x^2)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-y^'+1/4 y=9+e^{x/2}

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 9 + e^{\frac{x}{2}}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 36 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

Solution steps

y^{''} (x) - y^{'} (x) + \frac{1}{4} y = 9 + e^{\frac{x}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 36 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 36 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

4 y^{^{''}} + y + 2 = 0, y (0) = 0, y^{^{'}} (0) = \frac{1}{2}

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

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

(D^{2} + 1) y = csc (x)

y^{^{''}} + 5 y^{^{'}} + 4 y = 1

What is the solution for y^{''}-y^'+1/4 y=9+e^{x/2} ?
The solution for y^{''}-y^'+1/4 y=9+e^{x/2} is y=c_{1}e^{x/2}+c_{2}e^{x/2}x+36+(e^{x/2}x^2)/2