CoCalc Shared Fileslatex-tests / latexmk.tex
Author: Harald Schilly
1\documentclass{scrartcl}
2\title{Title of Document}
3\author{Name of Author}
4\usepackage{blindtext}
5
6\begin{document}
7\maketitle
8
9\blindmathtrue
10
11asdf.
12
13The incorporation of the boundary conditions yield two additional equations. -1 point
14
15
16                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  b. We know that $y(x)= c_1 x^1 + c_2 x^2 \ldots C_{N+1}x^{N+1}$.  We also have  $y''(x) = 2c_2 +6c_3 \ldots N(N+1)c_{N+1}X^{N-1}$
17We have $y(0) = y(1) = 0.$ We can say that $c_0 =0$ and $c_1 +c_2 + \ldots C_{N+1}$. From the equation given we have $y''(x) -\exp (y(x)) =0.$ We can evaluate each N equation at each grid points: We have the following: we have $h = \frac{1}{N+1}$
18
19 $$2 c_2 + 6 c_3 h + \ldots N(N-1)c_{N+1} h^{(N-1)} - [\exp(c_1 h^1 + c_2 h^2 \ldots C_{N+1}h^{N+1}]$$
20           $$\vdots$$
21$$2 c_2 + c_3 Nh + \ldots N(N-1)c_{N+1} {Nh}^{(N-1)} - [\exp(c_1 Nh + c_2 {Nh}^2 \ldots C_{N+1}{Nh}^{N+1}]$$
22
23
24\Blinddocument
25
26\end{document}
27
28%sagemathcloud={"latex_command":"latexmk -pdf -bibtex -pdflatex='pdflatex --interact=nonstopmode --synctex=1 %O %S' 'latexmk.tex'"}
29