This document discusses finding power series solutions to Airy's equation (y'' - t*y = 0) using the method of series solutions. It shows that the solutions are of the form a0*Ai(t) + a1*Bi(t), where Ai and Bi are known as the Airy functions. These Airy functions form a fundamental set of solutions to Airy's equation and oscillate for negative t but behave exponentially for positive t.