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Mathematics, 10.09.2020 01:01 sophiaa23
Since f(x, y) = 1 + y2 and ∂f/∂y = 2y are continuous everywhere, the region R in Theorem 1.2.1 can be taken to be the entire xy-plane. Use the family of solutions in part (a) to find an explicit solution of the first-order initial-value problem y' = 1 + y2, y(0) = 0. y = Even though x0 = 0 is in the interval (−2, 2), explain why the solution is not defined on this interval. Since tan(x) is discontinuous at x = ± , the solution is not defined on (−2, 2).
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Since f(x, y) = 1 + y2 and ∂f/∂y = 2y are continuous everywhere, the region R in Theorem 1.2.1 can b...
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