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

###### Math

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

(e) None of the above

1. 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

1. 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

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