Let L[y] = \(x^{2} \frac{d^{2} y}{d x^{2}}+p x \frac{d y}{d x}+q y\), where p, q are real constants. Let y₁(x) and y₂(x) be two solutions of L[y] = 0, x > 0, that satisfy y₁(x₀) = 1, \(y_{1}^{\prime}\)(x₀) = 0, y₂(x₀) = 0 and \(y_{2}^{\prime}\)(x₀) = 1 for some x₀ > 0. Then,

y₁(x) is not a constant multiple of y₂(x)

y₁(x) is a constant multiple of y₂(x)

1, ln x are solutions of L[y] = 0 when p = 1, q = 0

x, ln x are solutions of L[y] = 0 when p + q ≠ 0

Let L[y] = \(x^{2} \frac{d^{2} y}{d x^{2}}+p x \frac{d y}{d x}+q y\), where p, q are real constants. Let y1(x) and y2(x) be two solutions of L[y] = 0, x > 0, that satisfy y1(x0) = 1, \(y_{1}^{\prime}\)(x0) = 0, y2(x0) = 0 and \(y_{2}^{\prime}\)(x0) = 1 for some x0 > 0. Then,