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Fri Jan 20 18:11:44 2012 UTC (16 months ago) by jonathan rogness
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Updating Problems form calculusStewartCCC

    1 #DESCRIPTION
2 ##  Calculus: Second-order nonhomogeneous linear equations
3 ##ENDDESCRIPTION
4
5 ##KEYWORDS('calculus', 'differential equations', 'linear equations', 'second-order', 'nonhomogeneous', 'method of undetermined coefficients')
6
7 ## DBsubject('Calculus')
8 ## DBchapter('Second-Order Differential Equations')
9 ## DBsection('Nonhomogeneous Linear Equations')
10 ## Date('06/21/2011')
11 ## Author('Justin Sukiennik')
12 ## Institution('University of Minnesota')
13 ## TitleText1('Calculus: Concepts and Contexts')
14 ## EditionText1('4 Custom UMTYMP Ed.')
15 ## AuthorText1('Stewart')
16 ## Section1('17.2')
17 ## Problem1('')
18
19 #####################################################################
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23   "PGstandard.pl",
24   "MathObjects.pl",
25   "PGcourse.pl",
26 );
27
28 #####################################################################
30
31 $showPartialCorrectAnswers = 0; 32 33 TEXT(beginproblem()); 34 35 ##################################################################### 36 37 Context("Numeric"); 38 Context()->strings->add(A=>{},B=>{},C=>{},D=>{},E=>{},F=>{}); 39 40 ##################################################################### 41 42$a = Compute("2");
43 $b = random(1,2,1); 44 45 ##################################################################### 46 47 if ($b ==1){
48 $f = "\frac{d^2y}{dx^2}+4y=x-\frac{x^2}{20}"; 49$ans1 = "A";
50
51 $g = "\frac{d^2y}{dx^2}+6 \frac{dy}{dx}+8y=e^{2x}"; 52$ans2 = "B";
53 }
54 if ($b ==2){ 55$f = "\frac{d^2y}{dx^2}-5 \frac{dy}{dx}+6y=e^{2x}";
56 $ans1 = "E"; 57 58$g = "\frac{d^2y}{dx^2}+4y=-3x^2+2x+3";
59 $ans2 = "A"; 60 } 61 62 ##################################################################### 63 64$c = random(1,2,1);
65
66 if ($c ==1){ 67$h = "y''+4y'+20y = -3 \sin 2x";
68 $ans3 = "C"; 69 } 70 if ($c ==2){
71 $h = "y''+4y'+13y = 3 \cos 2x"; 72$ans3 = "C";
73 }
74
75 #####################################################################
76
77 $d = random(1,2,1); 78 79 if ($d ==1){
80 $i = "y''-2y'-15y = e^{3x}\cos 2x"; 81$ans4 = "F";
82 }
83 if ($d ==2){ 84$i = "y''-2y'-15y = 3x\cos 2x";
85 $ans4 = "D"; 86 } 87 88 ##################################################################### 89 90 Context()->texStrings; 91 BEGIN_TEXT 92 Match the following guess solutions $$y_p$$ for the$BITALIC method of undetermined coefficients$EITALIC with the second-order nonhomogeneous linear equations below.$PAR
93 $BCENTER 94$BBOLD A. $EBOLD $$\displaystyle y_p(x) = Ax^2+Bx+C$$,$SPACE
95 $BBOLD B.$EBOLD $$\displaystyle y_p(x) = Ae^{a x}$$, $SPACE 96$BBOLD C. $EBOLD $$\displaystyle y_p(x) = A \cos a x + B \sin a x$$,$BR
97 $BBOLD D.$EBOLD $$\displaystyle y_p(x) = (Ax + B)\cos a x + (Cx+D)\sin a x$$ $SPACE 98$BBOLD E. $EBOLD $$\displaystyle y_p(x) = A x e^{a x},$$ 99$SPACE and $SPACE 100$BBOLD F. $EBOLD $$\displaystyle y_p(x) = e^{3x}(A \cos a x + B \sin a x)$$ 101$ECENTER
102 $PAR 103$HR
104 $BBOLD 1.$EBOLD\{ans_rule(3)\} $$\displaystyle f$$
105 $PAR 106$BBOLD 2. $EBOLD\{ans_rule(3)\} $$\displaystyle g$$ 107$PAR
108 $BBOLD 3.$EBOLD\{ans_rule(3)\} $$\displaystyle h$$
109 $PAR 110$BBOLD 4. $EBOLD\{ans_rule(3)\} $$\displaystyle i$$ 111$PAR
112 $HR 113 END_TEXT 114 Context()->normalStrings; 115 116 ##################################################################### 117 118 ANS(str_cmp($ans1,"ignore_case"));
119 ANS(str_cmp($ans2,"ignore_case")); 120 ANS(str_cmp($ans3,"ignore_case"));
121 ANS(str_cmp(\$ans4,"ignore_case"));
122
123 ENDDOCUMENT();        # This should be the last executable line in the problem.