2. Seek a power series solution of the form y(r) =ana" to the differential equation n=0 y"(r) – 2ry (x) – 4y(x) = 0, xo = 0. (a) Set-up a recurrence for the cofficients, an. (b) Find the first four...

Extracted text: 2. Seek a power series solution of the form y(r) =ana" to the differential equation n=0 y"(r) – 2ry (x) – 4y(x) = 0, xo = 0. (a) Set-up a recurrence for the cofficients, an. (b) Find the first four terms of two independent power series solutions yı and y2 in such a way that you can write y(r) = a0y1(x) + a1y2(x). (c) Determine the Taylor series of e about the point ro = 0. %3D (Hint: Use the Taylor series for e".) (d) By using Part(c), find the explicit form of y2(x).