Part BCSIR NET December 2024complex-indices-make-it-oscillate-in-log-u

Complex indices make it oscillate in log u

For any non-zero solution y = y(x) of the differential equation $(2 x + 3)^{2} (d^{2} y /$ dx $^{2}) + 6 (2 x + 3) ($ dy/dx) + 8y = 0, x > 0, denote S := { $x \in (0, \infty) : y (x) = 0$ }. Then

A.S is an empty set.
B.S is a non-empty finite set.
C.S is a countably infinite set.✓
D.S is an uncountable set.

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

Complex indices make it oscillate in log u

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