Ordinary and Singular Points for Differential Equation

بسم الله الرحمن الرحيم


Ordinary and Singular Points for Differential Equation


The general form for second order differential equation with variable coefficients is ;
(d^2 y)/(dx^2 )+p(x)dy/dx+q(x)y=0 …..(1)
The equation has ordinary point at x=a , if the functions p(x) ,q(x) written as Taylor Series on x=a
p(x)=c_0+c_1 (x-a)+c_2 (?x-a)?^2+?
q(x)=b_0+b_1 (x-a)+b_2 (?x-a)?^2+?
If not then the equation has singular point at x=a , i.e if the functions p(x) ,q(x) can t written as Taylor Series on x=a .

















The general form for second order differential equation with variable coefficients is ;
(d^2 y)/(dx^2 )+p(x)dy/dx+q(x)y=0 …..(1)
The equation has ordinary point at x=a , if the functions p(x) ,q(x) written as Taylor Series on x=a
p(x)=c_0+c_1 (x-a)+c_2 (?x-a)?^2+?
q(x)=b_0+b_1 (x-a)+b_2 (?x-a)?^2+?
If not then the equation has singular point at x=a , i.e if the functions p(x) ,q(x) can t written as Taylor Series on x=a .





















The general form for second order differential equation with variable coefficients is ;
(d^2 y)/(dx^2 )+p(x)dy/dx+q(x)y=0 …..(1)
The equation has ordinary point at x=a , if the functions p(x) ,q(x) written as Taylor Series on x=a
p(x)=c_0+c_1 (x-a)+c_2 (?x-a)?^2+?
q(x)=b_0+b_1 (x-a)+b_2 (?x-a)?^2+?
If not then the equation has singular point at x=a , i.e if the functions p(x) ,q(x) can t written as Taylor Series on x=a .