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Homework answers / question archive / MATH 1)The equation 3( = 0 has two regular singular points x = 1 and x = 3

**MATH **

**1)**The equation 3(

= 0 has

- two regular singular points
*x*= 1 and*x*= 3. - one regular singular points
*x*= 1 and one irregular singular point*x*= 3. - one regular singular point
*x*= 1. - one regular singular point
*x*= 3. - no singular points.

*x*^{2}*y*^{00 }− 8*xy*^{0 }+ 9*y*= 0 for*x*6= 0 is

(e) None of the above

- The general solution of
*x*^{2}*y*^{00 }−*xy*^{0 }− 3*y*= 0 for*x*6= 0 is

(*a*) *C*_{1}|*x*| + *C*_{2}|*x*|^{−3 }(*b*) *C*_{1}|*x*|^{−1 }+ *C*_{2}|*x*|^{3 }(*c*) |*x*|(*C*_{1 }+ *C*_{2 }ln|3*x*|)

(*d*) |*x*|^{−1 }[*C*_{1 }cos(3ln|*x*|) + *C*_{2 }sin(3ln|*x*|)] (e) None of the above

2

- The differential equation
*xy*^{00 }− 2*xy*^{0 }− 2*y*= 0 has a regular singular point*x*_{0 }= 0 and a power series solution near*x*_{0 }= 0.

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

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