Part CCSIR NET June 2024differentiate-the-radius-not-the-components

Differentiate the radius not the components

If $x_{1} = x_{1} (t), x_{2} = x_{2} (t)$ is the solution of the initial value problem e^(−t) dx $_{1} /$ dt $= - x_{1} + x_{2}, e^{(} - t)$ dx $_{2} /$ dt $= - x_{1} - x_{2}, x_{1} (0) = 1, x_{2} (0) = 0$ , and $r (t) = x_{1}^{2} (t) + x_{2}^{2} (t)$ , then which of the following statements are true?

A.r(t) → 0 as $t \to + \infty$ ✓
B.r(ln 2) = e⁻ $^{1}$ ✓
C.r(ln 2) = 2e⁻ $^{1}$
D.r(t)eᵗ → 0 as $t \to + \infty$ ✓

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

Differentiate the radius not the components

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