Part CCSIR NET December 2024both-roots-negative-leaves-nothing-to-grow

Both roots negative leaves nothing to grow

Consider the non-homogeneous ordinary differential equation (ODE $) d^{2} y /$ dx $^{2} + 5$ dy/dx + 6y = sin(e^(−5x)), x > 0. Then which of the following statements are true?

A.Every solution of the ODE is bounded on $(0, \infty)$ ✓
B.There exists a solution of the ODE which is unbounded on $(0, \infty)$
C.Every solution of the ODE is unbounded on $(0, \infty)$
D.Every solution of the ODE tends to zero as $x \to \infty$ ✓

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: W(f, g) ≡ 0 implies f and g are linearly dependent

Both roots negative leaves nothing to grow

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