Part CCSIR NET June 2024equilibria-fence-every-solution-in

Equilibria fence every solution in

Consider the initial value problem (IVP $) y^{'} (x) = sin (y (x)) / (1 + y^{4} (x))$ for $x \in R$ , with $y (0) = y_{0}$ . Then which of the following statements are true?

A.There is a positive $y_{0}$ such that the solution of the IVP is unbounded
B.There is a negative $y_{0}$ such that the solution of the IVP is bounded✓
C.For every $y_{0} \in R$ , every solution of the IVP is bounded✓
D.For every $y_{0} \in R$ , there is a solution to the IVP for all $x \in R$ ✓

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.

See pricing

50 are analysed free — try those first.

Related counterexample: Linearisation determines stability at every equilibrium

Equilibria fence every solution in

More on this topic