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

The undifferentiated term fixes the substitution

Suppose that the differential equation d2y/d^{2}y/dx2+P(x)^{2} + P(x)dy/dx +e(2x)y=0,x∈R+ e^(2x)y = 0, x \in \mathbb{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?

  1. A.e⁻ˣ(P(x) + 1) is a constant function on R\mathbb{R}✓ Correct
  2. B.e^(−2x)P(x) is a constant function on R\mathbb{R}
  3. C.s(x)=e(2x)/2,x∈Rs(x) = e^(2x)/2, x \in \mathbb{R}
  4. D.P(x) → 1 as x→∞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

More on this topic

The chapter behind this: Linear ODE, Wronskian and systems — free to read

From Ordinary Differential Equations › Linear ODE, Wronskian, variation of parameters, systems

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