試題詳解

十三、Continued from Problem 十二 . Solve the non-homogeneous second order differential equa-
tion
x²y"(x)-4xy'(x)+6y(x)=x³
by variation of parameters, i.e, set the particular solution as +
u₂(x)y₂(x), where y₁(x) and y₂(x) are homogeneous solutions. With initial conditions
y(1) = 0 and y'(1) = 1 for the complete solution y(x), which of the following statements
is/are true?
(A) The real valued solution y(x) exists only for t ＞ 0.
(B) y(2) = 2.
(C) 2y'(2) -3y(2) = 8.
(D) y'(3) -y(3) = 4.
(E) None of the above are true.