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| 1 : | jonathan r | 2714 | gness #DESCRIPTION |
| 2 : | gness ## Calculus: Second-order homogeneous linear equations | ||
| 3 : | gness ##ENDDESCRIPTION | ||
| 4 : | gness | ||
| 5 : | gness ##KEYWORDS('calculus', 'differential equations', 'linear equations', 'second-order', 'homogeneous') | ||
| 6 : | gness | ||
| 7 : | gness ## DBsubject('Calculus') | ||
| 8 : | gness ## DBchapter('Second-Order Differential Equations') | ||
| 9 : | gness ## DBsection('Second-Order Linear Equations') | ||
| 10 : | gness ## Date('06/20/2011') | ||
| 11 : | gness ## Author('Justin Sukiennik') | ||
| 12 : | gness ## Institution('University of Minnesota') | ||
| 13 : | gness ## TitleText1('Calculus: Concepts and Contexts') | ||
| 14 : | gness ## EditionText1('4 Custom UMTYMP Ed.') | ||
| 15 : | gness ## AuthorText1('Stewart') | ||
| 16 : | gness ## Section1('17.1') | ||
| 17 : | gness ## Problem1('7') | ||
| 18 : | gness | ||
| 19 : | gness ##################################################################### | ||
| 20 : | gness DOCUMENT(); # This should be the first executable line in the problem. | ||
| 21 : | gness | ||
| 22 : | gness loadMacros( | ||
| 23 : | gness "PGstandard.pl", | ||
| 24 : | gness "MathObjects.pl", | ||
| 25 : | gness "PGcourse.pl", | ||
| 26 : | gness ); | ||
| 27 : | gness | ||
| 28 : | gness ##################################################################### | ||
| 29 : | gness | ||
| 30 : | gness TEXT(beginproblem()); | ||
| 31 : | gness | ||
| 32 : | gness $showPartialCorrectAnswers = 1; | ||
| 33 : | gness | ||
| 34 : | gness ##################################################################### | ||
| 35 : | gness | ||
| 36 : | gness Context("Numeric"); | ||
| 37 : | gness | ||
| 38 : | gness $a = random(2,12,1); | ||
| 39 : | gness | ||
| 40 : | gness $ans = Compute("sqrt($a)"); | ||
| 41 : | gness | ||
| 42 : | gness ##################################################################### | ||
| 43 : | gness | ||
| 44 : | gness Context()->texStrings; | ||
| 45 : | gness BEGIN_TEXT | ||
| 46 : | gness The general solution to the second-order differential equation \(\displaystyle y''+ $a y = 0\) is in the form \(\displaystyle y(x) = c_1 \cos \beta x + c_2 \sin \beta x.\) Find the value of \(\beta,\) where \(\beta > 0.\) $PAR | ||
| 47 : | gness Answer: \(\beta = \) \{ans_rule(20) \} | ||
| 48 : | gness END_TEXT | ||
| 49 : | gness Context()->normalStrings; | ||
| 50 : | gness | ||
| 51 : | gness ##################################################################### | ||
| 52 : | gness | ||
| 53 : | gness ANS( $ans->cmp() ); | ||
| 54 : | gness | ||
| 55 : | gness ENDDOCUMENT(); # This should be the last executable line in the problem. |
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