FINAL -...

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Unformatted text preview: WWI/filinfililiZ/qMxflflflflfiflflflfifififi“ Final Exam DIFFERENTIAL EQUATIONS, Math 204 WINTER 2004 Name: ROUM USE ON! Y Show your work/ steps. Circle your answers. Professor Ruben Hayrapetyan Problem 1. pts) equation: Find the general solution of the following differential Problem 2. ( 3 pts) Find the general solution of the following differential equation: 3/ — 17(312 ~1)cos(:c) = 0. Problem 3. (4 pts) Solve the following initial—value problem: [By sin2(:cy) cos(:r,y) +1111", + 1] d$+ [3x sin2(xy) cos(a:y)] dy = 0, ;1,/(1) : 71' 6 . Problem 4. (4 pts) Solve the following initial—value problem: (11/ % 4x2 + 2:1:y + y2 dry _ :L'(27 + 1/) , 11(1)=1- Problem 5. (4 pts) Find a general solution of the following difi'erential equation: 1/” _ 6y/ + 9?] : $631“ Problem 6. (4 pts) Find a general solution of the following differential equation: Problem 7. (4 pts) A l—kilogram mass is attached to a spring whose con- stant is 4 N /m. The medium offers a resistance to the motion numerically equal to 4 times the instantaneous velocity. Find the equation of motion if the weight is released from rest 2 meters below the equilibrium position. Classify this motion as overdamped, critically damped, or underdamped. Problem 8. (4 pts) Use the L aplace transform to solve the following initial— Value problem: 2/” + 3:1/ + 22/ : te‘, 21(0) = 0, 1/(0) = 1' Table of Laplace Transforms m) : £‘1F _ 17(8) = fif f’(t> _T 81%) — W J fWRt) s"F(s) — Sn—lf(0) — Sn—Zf/(O) — . — Jim-Um) t”) If“, a > —1 F$1Lr at J_ 411 e tneat —P “1—5;”?— 7 F _(_8—0 n+ _J r€i1r1(a7§) cos(at) 1— . —‘ ‘ 2as tsm(at) r t 008(at) eat ein(bt) m l— e‘” (,os(bt) te‘” sin(bt) (I ‘ s~a ~17 756 t 005(bt) J 6(t — G) 6—68 m — amt — c) 50%) t T ‘ 0ff<t — T)g(7’>d7‘ £{f}£{9} n is a positive integer. 10 ...
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