Mathematics, 24.02.2020 23:32 rsimmons696

(a) Verify that y = tan (x + c) is a one-parameter family of solutions of the differential equation y' = 1 + y².
(b) Since f(x, y) = 1 + y² and ∂f/∂y = 2y are continuous everywhere, the region R 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. Even though xₒ = 0 is in the interval (-2, 2), explain why the solution is not defined on this interval.

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(a) Verify that y = tan (x + c) is a one-parameter family of solutions of the differential equation...

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