View of /branches/CSUN/DifferentalEquations/CSUN-Series_Solution1.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 
   14 loadMacros(
   15 "PGbasicmacros.pl",
   16 "PGanswermacros.pl",
   17 "PGauxiliaryFunctions.pl"
   18 );
   19 
   20 TEXT(&beginproblem);
   21 $showPartialCorrectAnswers = 1;
   22 
   23 $a = random(1, 10);
   24 
   25 $abs = "$g*sqrt(($a)**2 + ($b)**2 + ($c)**2)";
   26 
   27 BEGIN_TEXT
   28 
   29 Find two linearly independent solutions of \( y'' + $a xy = 0 \) of the form
   30 $BR$BR
   31 \( y_1 = 1 + a_3 x^3 + a_6 x^6 + \cdots \)
   32 $BR$BR
   33 \( y_2 = x + b_4 x^4 + b_7 x^7 + \cdots \)
   34 $BR$BR
   35 Enter the first few coefficients:
   36 $BR$BR
   37 \( a_3 = \)  \{ans_rule(15)\} $BR
   38 \( a_6 = \)  \{ans_rule(15)\} $BR$BR
   39 \( b_4 = \)  \{ans_rule(15)\} $BR
   40 \( b_7 = \)  \{ans_rule(15)\}
   41 
   42 END_TEXT
   43 
   44 ANS(num_cmp("-$a/6"));
   45 ANS(num_cmp("$a^2/180"));
   46 ANS(num_cmp("-$a/12"));
   47 ANS(num_cmp("$a^2/504"));
   48 
   49 ENDDOCUMENT();