(a) Find the value of A so that the equation y ' - xy - 6x = 0 has a solution of the form y(x) = A + Be^((x^2)/2) for any constant B. A=?(b) If y(0) = 5, find BB=?
问题描述：
(a) Find the value of A so that the equation y ' - xy - 6x = 0 has a solution of the form y(x) = A + Be^((x^2)/2) for any constant B.
A=?
(b) If y(0) = 5, find B
B=?
答
(a)
y ' - xy - 6x = 0
(A + Be^((x^2)/2))'-x(A + Be^((x^2)/2))-6x=0
Bxe^((x^2)/2))-Ax-Bx((x^2)/2))-6x=0
-Ax-6x=0
A=-6
(b)
y(x)=-6+Be^((x^2)/2)
y(0)=5,-6+B=5
B=11