I am looking for a text that gives a good exposition of power series solutions to second order equations with variable coefficients. My course I'm guessing focuses mainly on this section. My knowledge of power series and Taylor series is not great. But I'm in the process of rectifying this. In the meantime I need a text that puts emphasis on this section. Most of what I've come across focuses on systems of equations. Any help would be appreciated. This here is my entire syllabus.
Differential Equations II (30L, 2C)
Syllabus:Ordinary differential equations: Linear equations of the second order where the coefficients are functions of the independent variable; Ordinary points; Singular points; Regular singular points;Solution in series: Stability of the solutions; Solution of Laplace’s equation; Revision of Euler’s homogeneous form of the second order ordinary differential equations; Legendre’s equation; Legendre’s polynomials – their linear independence and recurrence relations; Bessel’s function.Introduction to Difference equations: Complementary functions and particular solutions. Assessment: End of semester examination.