View of /trunk/NationalProblemLibrary/Rochester/setDiffEQ10Linear2ndOrderNonhom/ur_de_10_15.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('differential equation' 'second order' 'linear' 'nonhomogeneous')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Second-Order Differential Equations')
   10 ## DBsection('Nonhomogeneous Linear Equations')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT() ;
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl",
   28 "PGdiffeqmacros.pl",
   29 ) ;
   30 ############
   31 
   32 $r = random(2,9,1);
   33 $sign = random(-1,1,2);
   34 $r = $r * $sign;
   35 
   36 $a = 1 - 2 * $r;
   37 $b = $r**2;
   38 
   39 $c = random(-10,10,1);
   40 $d = random(-5,5,1);
   41 
   42 $m = random(2,9,1);
   43 while ($m * ($m-1) + $m * $a + $b == 0) { $m = random(2,9,1);}
   44 
   45 $n = 1/($m * ($m-1) + $m * $a + $b);
   46 
   47 $c1 = $c - $n;
   48 
   49 if ( $d - $r * $c1 == 0 ) {
   50   $d = $d+1;
   51   $c1 = $c - $n;
   52 }
   53 
   54 $d1 = $d - $m * $n;
   55 
   56 $k1 = $c1;
   57 $k2 = $d1 - $r * $c1;
   58 
   59 $eq = FEQ("x^2 y'' + $a x y' + $b y = x^$m");
   60 $ans = FEQ("x**$r * ($k1 + $k2 * ln x) + $n x^$m");
   61 
   62 TEXT(beginproblem()) ;
   63 
   64 $showPartialCorrectAnswers = 1 ;
   65 
   66 BEGIN_TEXT
   67 
   68 Find \(y\) as a function of \(x\) if
   69 \[ $eq, \]
   70 \( y(1) = $c, \ \ y'(1) = $d. \)
   71 $BR
   72 \(y=\) \{ans_rule(80)\}
   73 
   74 END_TEXT
   75 
   76 ANS(fun_cmp($ans));
   77 
   78 ENDDOCUMENT() ;
   79 
   80 
   81 
   82 
   83 
   84 
   85 ##################################################