Part BCSIR NET December 2024the-undifferentiated-term-fixes-the-substitution

The undifferentiated term fixes the substitution

Suppose that the differential equation $d^{2} y /$ dx $^{2} + P (x)$ dy/dx $+ e^{(} 2 x) y = 0, x \in R$ transforms into a second order differential equation with constant coefficients under the change of independent variable given by s = s(x) satisfying (ds/dx)(0) = 1. Then which of the following statements is true?

A.e⁻ˣ(P(x) + 1) is a constant function on $R$ ✓
B.e^(−2x)P(x) is a constant function on $R$
C. $s (x) = e^{(} 2 x) /2, x \in R$
D.P(x) → 1 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

The undifferentiated term fixes the substitution

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