Unformatted text preview: 6. [Problem 23.4] Let x * be a ﬁxed point of the equation x n +1 = f ( x n ). Give an accurate deﬁnition of stability of x * . Prove that x * is stable if  f ( x * )  < 1 and unstable if  f ( x * )  > 1. Draw a cobweb diagram to illustrate stability in the case1 < f ( x * ) < 0. IV. Separable and exact equations 7. Solve the initial value problem y = 3 x 2 3 y 24 , y (1) = 0 , and ﬁnd the interval of the maximal solution. 8. [Problem 10.1] Check that the following equation is exact and hence solve it (ﬁnd a ﬁrst integral) (2 xysec 2 x ) dx + ( x 2 + 2 y ) dy = 0 . 1...
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 Spring '10
 323
 Approximation, Boundary value problem, cobweb diagram, qualitatively correct cobweb

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