midterm1sol

midterm1sol - Problem 1 (20 points) For the autonomous...

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Unformatted text preview: Problem 1 (20 points) For the autonomous equation y! = _ 4 1. find the solution with y(0) = 1 and its limit when it: approaches infinity; B __ CHIHC) H 41‘ (3+2 _ 6 rfizfle ' _ 2* H 14-641: Uga— t- fit“ I we?! @ A= “3‘ 4t \_.LC¥‘£' 3H6 2 Paige/4f? : 2 3+€¢t fi MM tam 31%) -——*> Z This page is far confirming Problem 1 if not finished. Problem 2 (15 points) Solve y’ = 2y + 64,910) = 2 by variation of parameter. Problem 3 (20 points) Solve _ (v.2 + 2uv)du -|— (1:2 — v2)dv = U by two difl'erent method. a a WWW”: W W 99 W Win/1. (K5 Let k; “V tun dAA=£€du+vdk “41%: £36sz m; Uglfiklr k3]: Luv—r C [(“Bkikg = V’— 3vzu— u7’= OGLM. Problem 4 (15 points) Solve y' + $23: = 0 by two different methods. LY} / i;an 1_ _' “3)”? if” “V- 13 -;('X; €W= C. ‘3': 09 WW aLy L 90V T: —X if :HKIAX Ulfi‘I'JEXH x1 J} gitefifc 3:0-635 Problem 5 (15 points) Solve (t + 3m + y = 6*, y(—5) = 10 and find existence of interval. Problem 6 (15 points) Find curves in the first quadrant such that each tangent is separated equally by the tangent point between two axes. J 0L)” 33. _ l ’ “If: _ M X01? “f 7d)!“~'—o ...
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midterm1sol - Problem 1 (20 points) For the autonomous...

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