Unformatted text preview: a is at most π/ 2. Note : The cosine as the solution to a second-order IVP may be assumed, as may its least positive zero. 4. Let f and g satisfy the initial value problems f 00 = f ; f (0) = 1 ,f (0) = 0 g 00 = g ; g (0) = 0 ,g (0) = 1 . Establish each of the following: (a) fg-f g = 0; (b) g = f, f = g ; (c) f 2-g 2 = 1; (d) if h satisﬁes the same IVP as f then h = f ; (e) f is even and g is odd. Note : It may be assumed that f is nowhere zero. 1...
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- Spring '11
- Derivative, Continuous function, arbitrary continuous function