MATH 1)The equation 3(                       = 0 has   two regular singular points x = 1 and x = 3

MATH

1)The equation 3(

                      = 0 has

1. two regular singular points x = 1 and x = 3.
2. one regular singular points x = 1 and one irregular singular point x = 3.
3. one regular singular point x = 1.
4. one regular singular point x = 3.
5. no singular points.

2.  The general solution of 4x²y⁰⁰ − 8xy⁰ + 9y = 0 for x 6= 0 is

     (e) None of the above

3. The general solution of x²y⁰⁰ − xy⁰ − 3y = 0 for x 6= 0 is

                                  (a) C₁|x| + C₂|x|⁻³                 (b) C₁|x|⁻¹ + C₂|x|³                  (c) |x|(C₁ + C₂ ln|3x|)

                                    (d) |x|⁻¹ [C₁ cos(3ln|x|) + C₂ sin(3ln|x|)]         (e) None of the above

2

4. The differential equation xy⁰⁰ − 2xy⁰ − 2y = 0 has a regular singular point x₀ = 0 and a power series solution near x₀ = 0.

1. [4] Show that r₁ = 1 and r₂ = 0 are the roots of the indicial equation.
2. [12] Find a power series solution, which corresponds to r₁ = 1.
3. [1] Give the first four terms of the series solution found in part