Unformatted text preview: x β y x 2 ΒΆ dx + 1 x dy = 0 β F ( x, y ) = Z Β± 1 x Β² dy = y x + h ( x ) β βF βx = β y x 2 + h ( x ) = x β y x 2 β h ( x ) = x β h ( x ) = x 2 2 , and a general solution is given by F ( x, y ) = y x + x 2 2 = C and x β‘ . (The latter has been lost in multiplication by Β΅ ( x ).) Substitution the initial values, y = 3 when x = 1, yields 3 1 + 1 2 2 = C β C = 7 2 . 98...
View
Full
Document
This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

Click to edit the document details