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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
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 Spring '11
 DELALLAVE
 Differential Equations, Equations

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