Part BCSIR NET December 2024the-second-solution-carries-a-power-not-a-constant

The second solution carries a power not a constant

Given that $y_{1}(x) = e^(2x)$ is a solution of the ordinary differential equation (ODE $) x d^{2}y/$ dx $^{2} - (3 + 4x)$ dy/dx + (4x + 6)y = 0, x > 0. Let $y_{2} = y_{2}(x)$ be the solution of the ODE satisfying the conditions $y_{2}(1) = e^{2}/4$ and (dy $_{2}/$ dx $)(1) = 3e^{2}/2$ . Then which of the following statements is true?

A. $y_{2}$ is a strictly increasing function on $(0, \infty)$ ✓ Correct
B. $e^(-2x)y_{2}(x) \to 1$ as $x \to \infty$
C. $y_{2}$ is a strictly decreasing function on $(0, \infty)$
D. $e^(-2x)y_{2}(x) \to 0$ 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, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

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

The second solution carries a power not a constant

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