## DESCRIPTION ## Calculus ## ENDDESCRIPTION ## KEYWORDS('differential equation' 'second order' 'linear' 'nonhomogeneous') ## Tagged by tda2d ## DBsubject('Calculus') ## DBchapter('Second-Order Differential Equations') ## DBsection('Nonhomogeneous Linear Equations') ## Date('') ## Author('') ## Institution('Rochester') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') DOCUMENT() ; loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGdiffeqmacros.pl", ) ; \$r = random(-9,-1,1) ; \$u = random(1,9,1) ; \$s = \$r + \$u ; \$B = - \$r - \$s ; \$C = \$r *\$s ; \$k = random(1,3,1) ; \$rr = \$s + \$k ; \$q0 = random(1,9,1) ; \$qq0 = \$q0 ; \$q0 = \$q0 *(\$rr - \$r)*\$k ; \$q1 =0 ; \$q2 = 0 ; \$A =1 ; \$m = random(1,9,1) ; \$n = random(1,9,1) ; ################ \$L = diffop(\$A,\$B,\$C) ; \$Exp = "e^{\$rr t}"; \$rhs = "\$q0 \,\$Exp " ; \$y = undeterminedExp (\$A,\$B,\$C,\$rr,\$q0,\$q1,\$q2) ; \$z = ivy(\$A,\$B,\$C,\$m - \$qq0,\$n - \$rr *\$qq0 ) ; \$ans = " \$y + \$z " ; TEXT(beginproblem()) ; \$showPartialCorrectAnswers = 1 ; BEGIN_TEXT Find the solution of \[ \$L = \$rhs \] with \( y(0) = \$m \) and \( y'(0) = \$n .\) \$BR \(y = \) \{ans_box(4,80)\} END_TEXT ANS(fun_cmp(\$ans, vars=>"t")) ; ENDDOCUMENT() ; ####### ################################################## my \$XML_INFORMATION = <<'END_OF_XML_TRAILER_INFO'; Webwork Team MTH163 Differential equations solves \$A y'' + \$B y' + \$C y = \$q0 exp(\$r t), \$A, \$B, \$C, \$q0, \$q1, \$q2, \$r are integers; \$A not zero; \$r is not a root of the char. poly.. setUndeterminedCoefficients/1.pg University of Rochester Differential Equation, Inhomogeneous, Undetermined coefficients, second order linear, constant coefficients setUndeterminedCoefficients/1.pg http://webhost.math.rochester.edu/mth163lib/discuss/msgReader\$442 20000719T09:39:52 442 true UndeterminedCoefficients 1 END_OF_XML_TRAILER_INFO ##################################################