Part BCSIR NET December 2024the-lipschitz-condition-is-in-y-not-x

The lipschitz condition is in y not x

The initial value problem dy/dx $= \sqrt$ |x − 1| sin y, y(0) = 1 has

A.a unique solution on $R$ ✓
B.infinitely many solutions on the interval (−2, 2)
C.a unique solution and its maximal interval of existence is $(- \infty, 1)$
D.no solution on the interval (−2, 2)

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

50 are analysed free — try those first.

Related counterexample: Every IVP has a unique solution

More on this topic

bounded rhs global existenceJune 2023
linear growth global existenceDecember 2023
equilibria trap solutionsDecember 2023
Part C questionDecember 2023
non lipschitz at one height onlyJune 2024

The chapter behind this: Existence, uniqueness and how far the solution extends — free to read

From Ordinary Differential Equations › Existence–uniqueness, Picard, Lipschitz

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