Differential Equations Lecture Work Solutions 1

Differential Equations Lecture Work Solutions 1 - CHAPTER 1...

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Unformatted text preview: CHAPTER 1 1 Introduction and Applications 1.1 Basic Concepts and Definitions Problems 1. Give the order of each of the following PDEs a. b. c. d. e. uxx + uyy = 0 uxxx + uxy + a(x)uy + log u = f (x, y ) uxxx + uxyyy + a(x)uxxy + u2 = f (x, y ) u uxx + u2 + eu = 0 yy ux + cuy = d 2. Show that u(x, t) = cos(x − ct) is a solution of ut + cux = 0 3. Which of the following PDEs is linear? quasilinear? nonlinear? If it is linear, state whether it is homogeneous or not. a. b. c. d. e. f. g. h. i. uxx + uyy − 2u = x2 uxy = u u ux + x uy = 0 u2 + log u = 2xy x uxx − 2uxy + uyy = cos x ux (1 + uy ) = uxx (sin ux )ux + uy = ex 2uxx − 4uxy + 2uyy + 3u = 0 ux + ux uy − uxy = 0 4. Find the general solution of uxy + uy = 0 (Hint: Let v = uy ) 5. Show that is the general solution of y u = F (xy ) + x G( ) x x2 uxx − y 2 uyy = 0 1 ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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