Mathematics · Differential Equations
Consider the ordinary differential equation (ODE): d2y/dx2 + (cos(x)) dy/dx + (sin(x)) y = 0. Let φ1(x) and φ2(x) be solutions of the ODE satisfying φ1(0) = 1, φ1'(0) = 0, and φ2(0) = 0, φ2'(0) = 1. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There exist a, b ∈ ℝ such that φ1(x + 2π) = aφ1(x) + bφ2(x).✓
- 2There are no constants a, b ∈ ℝ such that φ1(x + 2π) = aφ1(x) + bφ2(x).
- 3φ2(x + 4π) is also a solution of the ODE.
- 4φ1(x + 2π) is also a solution of the ODE.
Correct answer
There exist a, b ∈ ℝ such that φ1(x + 2π) = aφ1(x) + bφ2(x).
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