[math] \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow} \newcommand{\ddxof}[1]{\frac{d #1}{d x}} \newcommand{\ddx}{\frac{d}{dx}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\dydx}{\ddxof y} \newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}} \newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}} \newcommand{\dist}{\mathrm{distance}} \newcommand{\arccot}{\mathrm{arccot\:}} \newcommand{\arccsc}{\mathrm{arccsc\:}} \newcommand{\arcsec}{\mathrm{arcsec\:}} \newcommand{\arctanh}{\mathrm{arctanh\:}} \newcommand{\arcsinh}{\mathrm{arcsinh\:}} \newcommand{\arccosh}{\mathrm{arccosh\:}} \newcommand{\sech}{\mathrm{sech\:}} \newcommand{\csch}{\mathrm{csch\:}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\mathds}{\mathbb} [/math]

Find the general solution of each of the following differential equations.

• [math]\dydx - \frac2xy = 3x^2 + 4[/math]
• [math]x\dydx + 3y + x = 0[/math]
• [math]7y + 2x\dydx = x^7 + 2[/math]
• [math]\dydx + 2xy = 5x[/math]
• [math]\dydx - 8y = e^{2x} + 4[/math]
• [math]6x^2y + \dydx = x^2[/math]
• [math]y\cos x + \dydx = \cos x[/math]
• [math]\dydx + (2x+3)y = 8x + 12[/math]
• [math]\dydx + 2y = 3 \cos x[/math]
• [math]\dydx + \frac yx = 2e^{-x}[/math]
• [math]11y+x\dydx = ax^2+bx+c[/math]
• [math](D+9)y = \pi[/math]
• [math]\dydx + \frac3xy = \frac{e^{2x}}{x^3}[/math]
• [math]x^2\dydx + 5xy = \frac{\cos x}{x^3}[/math].