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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+y4(x))) y'(x) = \sin(y(x))/(1 + y^{4}(x)) for x∈Rx \in \mathbb{R}, with y(0)=y0y(0) = y_{0}. Then which of the following statements are true?

  1. A.There is a positive y0y_{0} such that the solution of the IVP is unbounded
  2. B.There is a negative y0y_{0} such that the solution of the IVP is bounded✓ Correct
  3. C.For every y0∈Ry_{0} \in \mathbb{R}, every solution of the IVP is bounded✓ Correct
  4. D.For every y0∈Ry_{0} \in \mathbb{R}, there is a solution to the IVP for all x∈Rx \in \mathbb{R}✓ Correct

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, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

Related counterexample: Linearisation determines stability at every equilibrium

More on this topic

The chapter behind this: Stability and phase portraits — free to read

From Ordinary Differential Equations › Stability and phase portraits

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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