c. Verify that P,(t) = et satisfies the equation of part (b).

d. It can be shown in a manner similar to parts

(a) and

(b) that the P()s must satisfy the system of differential equations P(t) = aP (1) aP(1) k = 1,2,3,... Verify that P(t)=e(at)k! satisfies the system. (This is actually the only solution.)