Angus Leeming wrote: > > Could you export the lyx file to latex and post this latex file together > with the associated 0lyxpreview.tex? >
Here it is. Thanks.
\batchmode %% LyX 1.3 created this file. For more info, see http://www.lyx.org/. %% Do not edit unless you really know what you are doing. \makeatletter [EMAIL PROTECTED]/home/yosef/school/madar//}} \makeatother \documentclass[twoside,english,hebrew]{article} \usepackage[latin1,cp1255]{inputenc} \usepackage{a4wide} \usepackage{fancyhdr} \pagestyle{fancy} \setlength\parskip{\medskipamount} \setlength\parindent{0pt} \makeatletter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands. %% Bold symbol macro for standard LaTeX users \newcommand{\boldsymbol}[1]{\mbox{\boldmath $#1$}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands. \usepackage{fancyhdr} \usepackage[ddmmyy]{datetime} \date{} \makeatletter [EMAIL PROTECTED]@fancyhead [EMAIL PROTECTED]@fancyhead#1#2#3#4#5}} [EMAIL PROTECTED]@fancyfoot [EMAIL PROTECTED]@fancyfoot#1#2#3#4#5}} \makeatother \renewcommand{\headrulewidth}{0pt} \renewcommand{\footrulewidth}{0.4pt} \fancyfoot{} \fancyfoot[C]{\thepage} \fancyfoot[L]{\L{\formatdate{\day}{\month}{\year}}} \fancyfoot[R]{\inputencoding{cp1255}יוסף מלר % \L{043467430}} \setlength{\headsep}{0mm} \setlength{\headheight}{0mm} \setlength{\topmargin}{0mm} \setlength{\voffset}{0mm} \usepackage{babel} \makeatother \def\lyxlock{} \newcommand{\vieta}[3]{\left\{ \protect\begin{array}{l} #1_{1}+#1_{2}=#2\protect\\ #1_{1}#1_{2}=#3\protect\end{array}\right.} \usepackage[active,delayed,dvips,tightpage,showlabels,lyx]{preview} \AtBeginDocument{\AtBeginDvi{% \special{!userdict begin/bop-hook{//bop-hook exec <000000faf1e4>{255 div}forall setrgbcolor clippath fill setrgbcolor}bind def end}}} \begin{document} \begin{preview} $r^{2}-2r-3=0\rightarrow\left\{ \begin{array}{l} r_{1}+r_{2}=2\\ r_{1}r_{2}=-3\end{array}\right.\rightarrow r_{1}=-1,\, r_{2}=3\rightarrow y_{1}=e^{-x},\, y_{2}=e^{3x}$ \end{preview} \begin{preview} $y=C_{1}e^{-x}+C_{2}e^{3x}+y_{p}$ \end{preview} \begin{preview} $y"_{p}=4Ae^{2x}\leftarrow y'_{p}=2Ae^{2x}\leftarrow y_{p}=Ae^{2x}$ \end{preview} \begin{preview} $A=-1\leftarrow y"_{p}-2y'_{p}-3y_{p}=4Ae^{2x}-4Ae^{2x}-3Ae^{2x}=-3Ae^{2x}=3e^{2x}$ \end{preview} \begin{preview} $y=C_{1}e^{-x}+C_{2}e^{3x}-e^{2x}$ \end{preview} \begin{preview} $y_{p}=\left(Ax+B\right)e^{2x}$ \end{preview} \begin{preview} $y'_{p}=2e^{2x}\left(Ax+B\right)+Ae^{2x}$ \end{preview} \begin{preview} $y"_{p}=4e^{2x}\left(Ax+B\right)+4Ae^{2x}$ \end{preview} \begin{preview} \begin{eqnarray*} y"_{p}-2y'_{p}-3y_{p} & = & 4e^{2x}\left(Ax+B\right)+4Ae^{2x}-4e^{2x}\left(Ax+B\right)-2Ae^{2x}-3\left(Ax+B\right)e^{2x}=\\ & = & -3Axe^{2x}+\left(2A-3B\right)e^{2x}=-3xe^{2x}\end{eqnarray*} \end{preview} \begin{preview} $A=1\leftarrow-3A=-3$ \end{preview} \begin{preview} $B=\frac{2}{3}\leftarrow2-3B=0\leftarrow2A-3B=0$ \end{preview} \begin{preview} $y=C_{1}e^{-x}+C_{2}e^{3x}+\left(x+\frac{2}{3}\right)e^{2x}$ \end{preview} \begin{preview} $y_{1}=1,\, y_{2}=e^{-x}\leftarrow r_{1}=0,\, r_{2}=-1\leftarrow r^{2}+r=0$ \end{preview} \begin{preview} $y=C_{1}e^{-x}+C_{2}+y_{p}$ \end{preview} \begin{preview} $y_{p}=Ax+B\sin\left(4x\right)+C\cos\left(4x\right)$ \end{preview} \begin{preview} $y'_{p}=A+4B\cos\left(4x\right)-4C\sin\left(4x\right);\, y"_{p}=-16B\sin\left(4x\right)-16C\cos\left(4x\right)$ \end{preview} \begin{preview} \begin{eqnarray*} y"_{p}+y'_{p} & = & -16B\sin\left(4x\right)-16C\cos\left(4x\right)+A+4B\cos\left(4x\right)-4C\sin\left(4x\right)=\\ & = & A+\sin\left(4x\right)\left(-16B-4C\right)+\cos\left(4x\right)\left(-16C+4B\right)=3+4\sin\left(4x\right)\end{eqnarray*} \end{preview} \begin{preview} $\left[\begin{array}{lrrl} 1 & 0 & 0 & 3\\ 0 & -16 & -4 & 4\\ 0 & 4 & -16 & 0\end{array}\right]\rightarrow\left[\begin{array}{lrrl} 1 & 0 & 0 & 3\\ 0 & -16 & -4 & 4\\ 0 & 4 & -16 & 0\end{array}\right]\rightarrow A=3;\, B=-\frac{4}{17};\, C=-\frac{1}{17}$ \end{preview} \begin{preview} $y=C_{1}e^{-x}+C_{2}+3-\frac{16}{17}\cos\left(4x\right)+\frac{4}{17}\sin\left(4x\right)=C_{1}e^{-x}+C_{2}-\frac{16}{17}\cos\left(4x\right)+\frac{4}{17}\sin\left(4x\right)$ \end{preview} \begin{preview} $r=-1\leftarrow r^{2}+2r+1=\left(r+1\right)^{2}=0$ \end{preview} \begin{preview} $y_{1}=e^{-x};\, y_{2}=xe^{-x}$ \end{preview} \begin{preview} $y=C_{1}e^{-x}+C_{2}xe^{-x}+y_{p}$ \end{preview} \begin{preview} $y_{p}=Ax^{2}e^{-x}$ \end{preview} \begin{preview} $Ax^{2}$ \end{preview} \begin{preview} $y'_{p}=2Axe^{-x}-Ax^{2}e^{-x}$ \end{preview} \begin{preview} $y"_{p}=-2Axe^{-x}+2Ae^{-x}-2Axe^{-x}+Ax^{2}e^{-x}=Ax^{2}e^{-x}-4Axe^{-x}+2Ae^{-x}$ \end{preview} \begin{preview} $y"_{p}+2y'_{p}+y=Ax^{2}e^{-x}-4Axe^{-x}+2Ae^{-x}+4Axe^{-x}-2Ax^{2}e^{-x}+Ax^{2}e^{-x}=2Ae^{-x}=2e^{-x}\rightarrow A=1$ \end{preview} \begin{preview} $y=C_{1}e^{-x}+C_{2}xe^{-x}+2e^{-x}$ \end{preview} \begin{preview} $r^{2}+r-2=0\rightarrow\vieta{r}{-1}{-2}\rightarrow r_{1}=-2,\, r_{2}=1$ \end{preview} \begin{preview} $y_{1}=e^{x},\, y_{2}=e^{-2x}\rightarrow y'_{1}=e^{x},\, y'_{2}=-2e^{-2x}$ \end{preview} \begin{preview} $y=C_{1}e^{x}+C_{2}e^{-2x}+y_{p}$ \end{preview} \begin{preview} $y_{p}=Ax+B$ \end{preview} \begin{preview} $y'_{p}=A,\, y"_{p}=0$ \end{preview} \begin{preview} $y"_{p}+y'_{p}+y=A+Ax+B=2x\rightarrow A=2,\, B=-2$ \end{preview} \begin{preview} $y=C_{1}e^{x}+C_{2}e^{-2x}+2x-2$ \end{preview} \begin{preview} $y_{1}\left(0\right)=e^{0}=1;\, y_{2}\left(0\right)=e^{0}=1;\, y_{p}\left(0\right)=-2$ \end{preview} \begin{preview} $y'_{1}\left(0\right)=e^{0}=1;\, y'_{2}\left(0\right)=-2;\, y'_{p}\left(0\right)=2$ \end{preview} \begin{preview} $\left\{ \begin{array}{l} C_{1}y_{1}\left(0\right)+C_{2}y_{2}\left(0\right)+y_{p}\left(0\right)=0\\ C_{1}y'_{1}\left(0\right)+C_{2}y'_{2}\left(0\right)+y'_{p}\left(0\right)=1\end{array}\right.\rightarrow\left\{ \begin{array}{l} C_{1}+C_{2}=2\\ C_{1}-2C_{2}=-1\end{array}\right.\rightarrow\left(C_{1},C_{2}\right)=\left(1,1\right)$ \end{preview} \begin{preview} $y=e^{x}+e^{-2x}+2x-2$ \end{preview} \begin{preview} $r^{2}+4=0\rightarrow\vieta{r}{0}{4}\rightarrow r_{1}=2,\, r_{2}=-2$ \end{preview} \begin{preview} $y_{1}=e^{2x},\, y_{2}=e^{-2x}\rightarrow y'_{1}=2e^{2x},\, y'_{2}=-2e^{-2x}$ \end{preview} \begin{preview} $y=C_{1}e^{2x}+C_{2}e^{-2x}+y_{p}$ \end{preview} \begin{preview} $x^{2}$ \end{preview} \begin{preview} $y_{p1}=Ax^{2}+Bx+C$ \end{preview} \begin{preview} $y'_{p1}=2Ax+B;\, y"_{p1}=2A$ \end{preview} \begin{preview} $y"_{p1}+4y_{p1}=2A+4Ax^{2}+4Bx+4C$ \end{preview} \begin{preview} $4A=1\rightarrow A=\frac{1}{4};\,2A+4B+4C=0$ \end{preview} \end{document}
madar_ex3.lyx
Description: application/lyx
