File r37/lisp/csl/html/r37_0167.html artifact 6cb6ef8ee1 part of check-in a57e59ec0d

<A NAME=ODESOLVE>

<TITLE>ODESOLVE</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>ODESOLVE</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
 <P>
<P>
The <em>odesolve</em> package is a solver for ordinary differential 
equations. At the present time it has still limited capabilities: 
<P>
<P>
1. it can handle only a single scalar equation presented as an 
 algebraic expression or equation, and 
<P>
<P>
2. it can solve only first-order equations of simple types, linear 
 equations with constant coefficients and Euler equations. 
<P>
<P>
These solvable types are exactly those for which Lie symmetry 
techniques give no useful information. 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>odesolve</em>(&lt;expr&gt;,&lt;var1&gt;,&lt;var2&gt;) 
<P>
<P>
<P>
<P>
&lt;expr&gt; is a single scalar expression such that &lt;expr&gt;=0 
is the ordinary differential equation (ODE for short) to be solved, or 
is an equivalent 
<A HREF=r37_0045.html>equation</A>. 
<P>
<P>
&lt;var1&gt; is the name of the dependent variable, 
&lt;var2&gt; is the name of the independent variable. 
<P>
<P>
A differential in &lt;expr&gt; is expressed using the 
<A HREF=r37_0148.html>df</A> 
operator. Note that in most cases you must declare explicitly 
&lt;var1&gt; to depend of &lt;var2&gt; using a 
<A HREF=r37_0192.html>depend</A> 
declaration -- otherwise the derivative might be evaluated to 
zero on input to <em>odesolve</em>. 
<P>
<P>
The returned value is a list containing the equation giving the general 
solution of the ODE (for simultaneous equations this will be a 
list of equations eventually). It will contain occurrences of 
the operator <em>arbconst</em> for the arbitrary constants in the general 
solution. The arguments of <em>arbconst</em> should be new. 
A counter <em>!!arbconst</em> is used to arrange this. 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
depend y,x;

% A first-order linear equation, with an initial condition

ode:=df(y,x) + y * sin x/cos x - 1/cos x$

odesolve(ode,y,x); 

  {y=arbconst(1)*cos(x) + sin(x)}

</TT></PRE><P>