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Part BCSIR NET June 2024repeated-root-needs-another-log

Repeated root needs another log

Let φ\varphi denote the solution to the boundary value problem (BVP) (xy′)′ − 2y′ + y/x = 1 for 1<x<e41 < x < e^{4}, with y(1) = 0 and y(e4)=4e4y(e^{4}) = 4e^{4}. Then the value of φ(e)\varphi(e) is

  1. A.−e/2✓ Correct
  2. B.−e/3
  3. C.e/3
  4. D.e

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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