Differential Equations 306 HW Week 12 Spring 2015

1. Power Series Solutions about Ordinary Points

8.1: 1-9 You should solve all problems 1-9 with 2 methods:1. separation of variables or integrating factors 2. power series;then show that these solutions are equivalent for problems 1-7 and 9. ( Omit showing the equivalence in 8.1: 8.)

8.1: 11-13 ; 8.2: 1-6

2. Ordinary, Regular and Irregular Singular Points

8.3: 1 – 8 Please identify singular points using the definition, as discussed in class.

3. Euler or Equidimensional Equation of Order 2

Find the general solution for the following differential equations. Please note that each has a RSP at x = 0 and that the interval of solution is x > 0.

a.

b.

c.

d.

e.

f.

g.

4. Method of Frobenius (These problems will probably be omitted from the HW.)

Each of the following differential equations has a regular singular point (RSP) at x = 0. Determine the indicial equation, the exponents of the singularity at 0, (i.e. the roots of the indicial equation) and the recurrence relation. Find the series solution for x > 0 corresponding to the larger root. If the indicial equation has a double root, find one solution.

a.

b.

c.

d,