For each of the following differential equations: ODE1. (2 + x)y" + (1+x)y' + 3y = 0 ODE2. x?y" + x(1+ x)y' – 3(3+x)y = 0 ODE3. x²(1+ x)y" – x(3 – x)y' + 4y = 0 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. 1. 2. Based on your results in (a), use the appropriate method to determine two linearly independent series solutions about x, = 0. Indicate, the indicial equation, the root(s) of the indicial equation, and the recurrence relation, where applicable. а. For ODE2, use formula (4.17) to determine its second series solution. Hint: substitute series for e-x b. For ODE3, verify that the first series solution can be written as: Y1 = -Σ-1)" (n + 1)*χn*2 In=0 Then, use formula (4.15) or (4.16) to determine its second series solution. 3. For all three equations, write the first four non-zero terms (unless it terminates earlier) of each series solutions, where relevant.