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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · ODE, PDE & Applied Mathematics › Ordinary Differential Equations

“W(f, g) ≡ 0 implies f and g are linearly dependent” — false

Counterexample: f(x) = x², g(x) = x|x| on ℝ

The Wronskian vanishes identically but no constant multiple relates them. The implication holds only for solutions of a common linear ODE.

ODEwronskian