3 Without Solving The Initial Value Problem Determine The Largest Interval In Which The Solution Of Tan X Y Y X 1 (137.29 KiB) Viewed 51 times
(3) Without solving the initial value problem, determine the largest interval in which the solution of (tan x)y' - y = x² y(5) = 2 exists and is unique.
(4) Consider the IVP y' = 1+ y² y(0) = 0. (a) Verify that y(x) = tan(x) is the solution to this IVP. (b) Both f(x, y) 1+ y² and fy(x, y) = 2y are continuous on the whole xy-plane. Yet the solution y(x) = tan(x) is not defined for all -∞ < x < ∞. Why does this not contradict the theorem on existence and uniqueness (Theorem 2.3.1 of Trench)? (c) Find the largest interval for which the solution to the IVP exists and is unique. =
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