Question

Determine the singular points o the differential equations Classify each singular point as regular or irregular.

Answer 1

\[(x^2+x-6)y''+(x+3)y'+(x-2)y=0\]

Answer 2

\[y''+\frac{1}{x-2}y'+\frac{1}{x+3}y=0\]

Answer 3

singular points at 2, and -3

Answer 4

\[(x-x_o)p(x)=0\]

\[(x-2)\frac{1}{x-2}=1=analytic\]

\[(x-x_0)^2q(x)=(x-2)^2\frac{1}{x+3}=analytic\]

2 is a regular singular point

\[(x+3)\frac{1}{x-2}|_{x=3}=analytic\]

\[(x+3)^2\frac{1}{x+3}=x+3|_{x=3}=analytic\]

2 and -3 are regular singular