View of /branches/CSUN/Differential_Equations/Series_Solution_1.pg

    1 ##DESCRIPTION
    2 #  Power series solution of a differential equation
    3 ##ENDDESCRIPTION
    4 
    5 ## DBsubject('Calculus')
    6 ## DBchapter('Second-Order Differential Equations')
    7 ## DBsection('Second-Order Linear Equations')
    8 ## KEYWORDS('power series solution')
    9 ## Author('David Protas')
   10 ## Institution('CSUN')
   11 
   12 DOCUMENT();
   13 loadMacros(
   14 "PGstandard.pl",
   15   "Parser.pl",
   16   "PGcourse.pl",
   17   "PGanswermacros.pl",
   18   "PGbasicmacros.pl",
   19 );
   20 
   21 Context("Numeric");
   22 TEXT(&beginproblem);
   23 $showPartialCorrectAnswers = 1;
   24 
   25 $a = random(1, 10);
   26 $abs = "$g*sqrt(($a)**2 + ($b)**2 + ($c)**2)";
   27 
   28 Context()->texStrings;
   29 BEGIN_TEXT
   30 
   31 Find two linearly independent solutions of \( y'' + $a xy = 0 \) of the form
   32 $BR$BR
   33 \( y_1 = 1 + a_3 x^3 + a_6 x^6 + \cdots \)
   34 $BR$BR
   35 \( y_2 = x + b_4 x^4 + b_7 x^7 + \cdots \)
   36 $BR$BR
   37 Enter the first few coefficients:
   38 $BR$BR
   39 \( a_3 = \)  \{ans_rule(15)\} $BR
   40 \( a_6 = \)  \{ans_rule(15)\} $BR$BR
   41 \( b_4 = \)  \{ans_rule(15)\} $BR
   42 \( b_7 = \)  \{ans_rule(15)\}
   43 
   44 END_TEXT
   45 
   46 Context()->normalStrings;
   47 ANS(num_cmp("-$a/6"));
   48 ANS(num_cmp("$a^2/180"));
   49 ANS(num_cmp("-$a/12"));
   50 ANS(num_cmp("$a^2/504"));
   51 
   52 ENDDOCUMENT();