(a) Whenever there is no surviving spouse of a deceased veteran entitled to dependency and indemnity compensation, dependency and indemnity compensation shall be paid in equal shares to the children of the deceased veteran at the following monthly rates:

(b) If dependency and indemnity compensation has been awarded under this section to a veterans child or children and the entitlement to dependency and indemnity compensation under this section of an additional child of that veteran who is over the age of eighteen years and who had previously been entitled to dependency and indemnity compensation under this section before becoming eighteen years of age is later reestablished effective retroactively upon determination that such child is pursuing a course of instruction at an approved educational institution, the amount payable retroactively to the additional child is the amount equal to the difference between the total of the increased award payable under this section to the children of the deceased veteran for the retroactive period and the prior total award for such purpose for that period.