Skip to content
Part CCSIR NET December 2024eliminate-first-then-read-the-eigenvalues

Eliminate first then read the eigenvalues

If x = x(t), y = y(t) is the solution of the initial value problem dx/dt + dy/dt = 2x − 3y + eᵗ, dx/dt + 2(dy/dt) = 3x − 4y + 2eᵗ, x(0) = −1, y(0) = −1/2, then which of the following statements are true?

  1. A.x(π)=−eπ,y(π)=1/2x(\pi) = -e^\pi, y(\pi) = 1/2✓ Correct
  2. B.x(−π)=e(−π),y(−π)=1/2x(-\pi) = e^(-\pi), y(-\pi) = 1/2
  3. C.x has infinitely many zeros in R\mathbb{R}✓ Correct
  4. D.y has infinitely many zeros in R\mathbb{R}✓ Correct

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

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram