q2a - AVWW‘P/f QUIZZ 2 MATH 2233 SECTION 2, SPRING 2011...

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Unformatted text preview: AVWW‘P/f QUIZZ 2 MATH 2233 SECTION 2, SPRING 2011 INSTRUCTOR: WEIPING LI' Print Name and Student # SHOW WORK FOR CREDIT !!! SHOW WORK FOR CREDIT H! (1) (lOpts) Find the general solution of the given differential equation 1/, + y = 5sin(2t), and u;:to determine how solution behaves ast—>+OO- ' 5PM H = f, F: ef ( ) =| Infeflmfwj {4% fl“) " e e; ' HW 565’ + 5 = 5 scncztrflt (Jay = 5 scnptyet 6‘3 5 3 J{n(2t)' Jaw =(s«‘n(2+> '2Coszt)ct+ C WEIPING LI (2) (10pts) (a) Draw a direction field for the equation ty/ + (t + 1)}; = 2te“t, y(1) = a, t > 0 How do solution appear to behave as t —> 0? Does the behave depend on the choice of the initial value a? Let a0 be the value of a for which the transition from one type of behavior to another occurs. 2t€t~lt+Q5 =2ét_ 1713 .t 'l: —’t (=9 2.6, “iii—Ht); I 1+, f: fl“):Q_ amd " T3“)=O +9 0 (b) Find the integration factor, solve the initial value problem and find the critical value a exactly. + 0 51,0041: 5 firth—‘— A—t lm’j f“dLW flit) " C = C 7,, = t+lnf ,t. C t = E z {:6 ti - flu") an yl-e t =26. tbetj)’: Zét‘tet : 2f tat-5 =J2t “it : tl+ C’ 2‘ - - "'1: =6L => C=ae—l 3;‘t€t+CT€ . 3“) _t 3 ._. ghee—0% (c) Describe the behave of the solution corresponding to the initial value no. ‘ . —t (1) if A? Jé [HM flu') = [HM 1‘6 + («e—1);. unbounded (2) if or <44: 31H.) decreasdfi unloanZF as f6 o 't e—>o +->c> ~b ' ' b t 91 Zer - ' ( 5 : r 0 (a) «f th—L‘ —aa , L305“) if)“; ’Ce 0 a”: one es‘lb _ I, ...
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q2a - AVWW‘P/f QUIZZ 2 MATH 2233 SECTION 2, SPRING 2011...

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