[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](D-2)^2y=4x^2-5[/math]
• [math](D^2-3D+2)y=4x+3[/math]
• [math]\deriv2y + \dydx - 2y = 5e^{-x}[/math]
• [math]D(D-2)y = 6x^2+2x-6[/math]
• [math](D^2+D-2)y = 6e^{-2x}[/math]
• [math](D^2+D-2)y=6e^{-2x} + 2x - 4[/math]
• [math](D^2+D-2)y = 6e^{-2x} + 15e^x[/math]
• [math]D^2(D+3)y = 5x-2[/math]
• [math]\deriv2y + 4y = 5 \cos 3x[/math]
• [math]\deriv2y + 9y = 2 \sin 3x[/math]
• [math](D^2+1)y = 10 \sin x + 3e^{-x}[/math]
• [math](D^2+1)y = 4\sin x + 8\cos x[/math]
• [math](D^2-2D+1)y = 3e^x \sin x[/math]
• [math](D^2+2D+2)y = 3e^x \cos x[/math].