Let L(y) = y + by' + cy = 0 have solution u1 and u2, and let

Question:

Let L(y) = y" + by' + cy = 0 have solution u1 and u2, and let yp = v1u1 + v2u2. Show that
L(yp) = v1(u"1 + bu'1 + cu1) + v2(u"2 + bu'2 + cu2)
+ b(v'1u1 + v'2u2) + (v'1 u1 + v'2u2)' + (v'1u'1 + v'2u'2)
Thus, if the conditions of the method of variation of parameters hold?