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hw2solution - Assignment 2 Math 427K Due Wednesday February...

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Unformatted text preview: Assignment 2 Math 427K Due Wednesday, February 3, 20010 To obtain full credit, you must show all your work. Your assignments will not be accepted unless they are legible, neat, and stapled. Problem 1. Solve problems 13 to 20 from Chapter 2, Section 1 of the course textbook. Problem 2. Use separation of variables to find the general solution. Then, obtain the particular solution satisfying the given initial condition. a) y’ — 33026—11 2 0, y(0) = 0 b) y’ = (312 — y) 6". 11(0) = 2 C) y’ = 6“”, y(0) =1 d) y’ = y(y — 2), y(0) = 4 Problem 3. Show that equation is exact and obtain its general solution. Also, find the particular solution corresponding to the given initial condition. a) (sin(a:y) + xycos(my))dx + x2 cos(:cy) dy = 0, y(2) = —1 b) (3 x2 sin(2y) — 2:1: y) d2: + (2363 cos(2y) — x2) dy = 0, y(1/2) = 3.1 c) 3x2 y ln(y) d2: + (m3 ln(y) + m3 — 2 y) dy = 0, 111(8) = 3 d) 3dx —dy= 0, y(0) = 6 Problem 4. (Euler’s Method.) Use the Euler method to compute, by hand, y1, 312 and 313 for the specified initial value problem using h = 0.2. a) y’ = ~21. y(0) = 1 b) y' 2 1+ 237112, y(1) = —2 C) y’ = :82 — :12, y(3) = 5 d) y’ = tan(a: + 31), y(1) = 2 e)y’=x/?v’+_, y(0)=3 WW3) : 3 9/4! q; 'f 73%?) ”73) , N = 43%} Wkly 9?] {D L’(j);«>3 2:) N7 =v7vrc ,3 JL’XJ) “(33193 »J ’l 4WL ”3(8) 5 , M 1”“ g!) S}? — a} C C; t§5é}~§——7 Mink 4% $0M“ ‘3 ...
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