x²(1+ x)y" – x(3 – x)y' + 4y = 0 a) Determine if xo = 0 is an ordinary or a singular point. If it is a singular point, determine if it is a regular or an irregular singular point. b) Based on your...

Extracted text: x²(1+ x)y" – x(3 – x)y' + 4y = 0 a) Determine if xo = 0 is an ordinary or a singular point. If it is a singular point, determine if it is a regular or an irregular singular point. b) Based on your results in (a), use the appropriate method to determine two linearly independent series solutions about xo = 0. Indicate, the indicial equation, the root(s) of the indicial equation, and the recurrence relation, where applicable. Verify that the first series solution can be written as: 00 (-1)"(n + 1)²x"+2 In=0 Then, use formula (Eqn. 1) or (Eqn. 2) to determine its second series solution. If r1 – r2 = 0, y2(x) = y1(x) In |x| + E=1Anxn+ri (Eqn. 1) If r1 - r2 = Positive Integer, y2(x) = k y1(x) In |x| + E-o Bnx"+r2 (Eqn. 2)