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Unformatted text preview: or y ( x ) 4 x = 0 4 x = 0 . Thus x = 0, which is a contradiction. (c) Taking C = 0 in the implicit solution 4 x 2 y 2 = C given in Example 5 on page 9 gives 4 x 2 y 2 = 0 or y = 2 x . Both solutions y = 2 x and y = 2 x satisfy y (0) = 0. EXERCISES 1.3: Direction Fields, page 22 1. (a) or y = 2 x , dy dx = d dx ( 2 x ) = 2 a n d 4 x y = 4 x 2 x = 2 , x 6 = 0 . Thus y = 2 x and y = 2 x are solutions to the dierential equation dy/dx = 4 x/y on any interval not containing the point x = 0. (b) , (c) See igures B.1 and B.2 in the answers of the text. 10...
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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