試題詳解

12. For the following homogeneous second order linear differential equation
(x²-1)y"(x)-2xy''(x)+2y(x)=0
for x ＞ 1, given one solution y₁(x) = x, the other linearly independent solution y₂(x) can
then be derived by setting y₂(x) = v(x)y₁(x). Which of the following statements is/are
true?
(A)(x³+x)v"(x)+2v'(x)=0.
(B) u(x) with u'(x) = corresponds to one of the possible solutions.
(C) u(x) with u'(x) = corresponds to one of the possible solutions.
(D) y(x) = 1 + x + x² is one of the possible solutions.

(E) None of the above is true.