Verify by direct substitution that the given power series is a particular solution of the indicated differential equation. a. y = sigma^infinity_n = 0 (-1)^n/n! x^2n, y' + 2xy = 0
b. y = sigma^infinity_n = 0 (-1)^n x^2n, (1 + x^2)y' + 2xy = 0
c. y = sigma^infinity_n = 1 (-1)^n + 1/n x^n, (x + 1)y" + y' = 0
d. y = sigma^infinity_n = 0 (-1)^n/2^2n (n!)^2 x^2n, xy" + y' + xy = 0

Tom is the deli manager at a grocery store. he needs to schedule employee to staff the deli department for no more that 260 person-hours per week. tom has one part-time employee who works 20 person-hours per week. each full-time employee works 40 person-hours per week. write and inequality to determine n, the number of full-time employees tom may schedule, so that his employees work on more than 260 person-hours per week. graph the solution set to this inequality.