HW2Key - Assignment #2 Due: At the START of tutorial on...

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Unformatted text preview: Assignment #2 Due: At the START of tutorial on June 1, 2011. No late assignments will be accepted. 1. Solve the following differential equations (a) :cln(:c)% + y 2 21min (b) w 2 mew + (c) (2x+y+1)f—}g— = 1 (d) ydx + (2mg — e”2y)dy = 0 2. (a) Show that we can transform the differential equation dy 36% into a linear differential equation by using the substitution 2 lug. (b) Use this method to solve + P($)y = Q($)y1ny d 93—y22x2y + ylny dcc 3. A Riccati equation is a differential equation with the form / y = 17(90) + qtr)?! + r(w)y2 (a) Suppose we are able to find a particular solution yl Show that by using the substitution y($) = y1(m)+u(x) you can transform a Riccati equation into a Bernoulli’s equation. (b) Find one-parameter family of solutions for the differential equation d ~2+2$y=l+x2+y2 dm knowing that y1 2 LC is a solution. 4. (a) Find an implicit solution of IVP 2 2 dy y —x dx 339 ) y< ) f (b) Write the solution explicitly and give the largest interval I over which the solution is defined. .1) Spun /\ J7‘—%; D/K v [mi-K) '14» {, r 2, s a = .L. at, \ {A}: 2,1 S Jc/VL T w 2. .Lu: lL-fi C. ,4.) LASQwTQ 7L . :L 1 c. [A s- L ‘f L or 17‘ ‘83CQ, I 9. (3/3 Pcm1f5\iv1~l§4Y(*)\O «a! 0 (Viva sob-[(W- ‘yt/‘LW L , ’s “ Lu r ‘A) l «3! [DC 1+0\ )“B\ + C \3‘ O I? mu»); “Lb; »2\}U) D c“ SCLJM W / ((«u + URL“) ) <: P“; J? 0\w) (\6‘.(M{mu)) - 7.. + UK fofi) £\%\1 ) (’ ((m) —\— U‘wa) - P($)+\6(‘1Lv~) + an) {A 0/ / ~ W ' 11““ 51A : Y(V\)U\ (A __ kc‘L ) 12 L Mat wfl‘ “‘3 Z 621/14 owl-L3, 4L1“ ,(«3 (W7 M M MJLA $ ' 0/1‘ ~/\ 2. Uk/L : __ 7. 2.. _. ln\“\ 1' '5) Lkzr_L(n(nz+C 0 ...
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This note was uploaded on 01/15/2012 for the course MATH 201 taught by Professor Steacy during the Fall '10 term at University of Victoria.

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HW2Key - Assignment #2 Due: At the START of tutorial on...

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