試題詳解

16、Consider the following second order differential equation
3t²y''(t) + sin(t)y'(t) - cos(t)y(t) = 0.
Let y1(t) = t^r1be two linearly independent Frobenius series solution for y(t) in the above differential equation when t ＞ 0. Assuming r₁≥r₂ and a₀ = 1, which of the following statements is/are true regarding the solution y1(t)?
(A) r₁ = 1.
(B)
(C)
(D)
(E) None of the above is true.