Physics · Differential Equations
Let y be a solution of the ordinary differential equation (1 + x2)y'' + (1 + 4x2)y = 0 for x > 0, with initial condition y(0) = 0. Then, according to Sturm's comparison theorem, y has:
- 1at most 3n zeros in [0, nπ], ∀n ∈ &;ℕ
- 2at least n zeros in [0, nπ], ∀n ∈ &;ℕ
- 3infinitely many zeros in [1, ∞)✓
- 4infinitely many zeros in [0, 1]
Correct answer
infinitely many zeros in [1, ∞)
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