View of /trunk/NationalProblemLibrary/Rochester/setDiffEQ9Linear2ndOrderHomog/ur_de_9_19.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('differential equation' 'second order' 'linear')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Second-Order Differential Equations')
   10 ## DBsection('Second-Order Linear Equations')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 
   21 DOCUMENT() ;
   22 
   23 loadMacros(
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl",
   29 "PGdiffeqmacros.pl",
   30 ) ;
   31 ############
   32 
   33 $r = random(2,9,1);
   34 $sign = random(-1,1,2);
   35 $r = $r * $sign;
   36 
   37 $a = 1 - 2 * $r;
   38 $b = $r**2;
   39 
   40 $k1 = random(-10,10,1);
   41 $d = random(-5,5,1);
   42 if ( $d - $r * $k1 == 0 ) { $d = $d+1; }
   43 
   44 $k2 = $d - $r * $k1;
   45 
   46 $eq = FEQ("x^2 y'' + $a x y' + $b y = 0");
   47 $ans = FEQ("x**$r * ($k1 + $k2 * ln x)");
   48 
   49 TEXT(beginproblem()) ;
   50 
   51 $showPartialCorrectAnswers = 1 ;
   52 
   53 BEGIN_TEXT
   54 
   55 Find \(y\) as a function of \(x\) if \[ $eq, \]
   56 $BR
   57 \( y(1) = $k1, \ \ y'(1) = $d. \)
   58 $BR
   59 \(y=\)\{ans_rule(20)\}
   60 
   61 END_TEXT
   62 
   63 ANS(fun_cmp($ans));
   64 
   65 ENDDOCUMENT() ;
   66 
   67 
   68 
   69 
   70 
   71 
   72 ##################################################