試題詳解

十八、 For the following second order differential equation
tx"(t)+(4t-2)x'(t)+(2t-4)x(t)=0
Let x₁(t)= be the two linearly independent
Frobenius series solutions for x(t) when x ＞ 0, where ri and r₂ are the zeros of the
corresponding indicial equation. Assume r₁ ≥ r₂ and ao = b₀ = 1. Which of the following
statements is/are true?
(A) r₁ - r₂ is not an integer.
(B) .
(C)
(D) .
(E) None of the above are true.