 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-2-course-of-the-university-of-oxford/2007/7/iii/solution

x

leaves this autonomous differential equation unchanged. For every

c \geq 1

, the same formula

u_{c} (x) = {0, [3 (x - c) /4]^{4/3}, x \leq c, x \geq c

satisfies

u_{c} (1) = 0

, and the zero function does too. Thus solutions exist and are not unique, exactly as for the initial point

(0, 0)

. The relevant failure is the Lipschitz condition at

y = 0

; moving the initial value of

x

does not remove it.

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