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Diffstat (limited to 'src/input/nlode.input.pamphlet')
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diff --git a/src/input/nlode.input.pamphlet b/src/input/nlode.input.pamphlet new file mode 100644 index 00000000..fc088d79 --- /dev/null +++ b/src/input/nlode.input.pamphlet @@ -0,0 +1,64 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input nlode.input} +\author{The Axiom Team} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<<license>>= +--Copyright The Numerical Algorithms Group Limited 1994. +@ +<<*>>= +<<license>> +-------------------------- nlode.input -------------------------------- +)cl all +-- this will be the unknown +y := operator y + +-- some non-linear non-exact 1st order equations + +deq := (sin y x - x / y(x)) * differentiate(y x, x) = 1 +-- the result with no initial condition is a first integral +-- when equated to any constant +solve(deq, y, x) + +deq := differentiate(y x, x) = y(x) / (x + y(x) * log y x) +solve(deq, y, x) +-- same with initial condition y(1) = 1 +-- the result is a first integral if equated to 0 +solve(deq, y, x = 1, [1]) + +deq := (exp(- 2 * y x) - 2 * x * y x) * differentiate(y x, x) = y x +solve(deq, y, x) + +-- this one has an independent parameter w, initial condition y(0) = 0 +deq := differentiate(y x, x) = w + y(x) / (1 - y x) +solve(deq, y, x = 0, [0]) + +-- Bernoulli equation: the result is a first integral when equated to +-- any constant, but it can be explicitly solved for y(x) +deq := x**2 * differentiate(y x, x) + 2 * x * y x - y(x)**3 +solve(deq, y, x) + +-- Riccati equation: the result is a first integral when equated to +-- any constant, but it can be explicitly solved for y(x) +deq := differentiate(y x,x) = 1 + x**2 - 2 * x * y x + y(x)**2 +solve(deq, y, x) + +-- Riccati equation: the result is a first integral when equated to +-- any constant, but it can be explicitly solved for y(x) +deq := x**2 * differentiate(y x,x) = -1 - x * y x + x**2 * y(x)**2 +solve(deq, y, x) + + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |