Internal
problem
ID
[12661]
Book
:
Handbook
of
exact
solutions
for
ordinary
differential
equations.
By
Polyanin
and
Zaitsev.
Second
edition
Section
:
Chapter
2,
Second-Order
Differential
Equations.
section
2.1.2-5
Problem
number
:
161
Date
solved
:
Tuesday, January 28, 2025 at 08:03:24 PM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
✓ Solution by Maple
Time used: 0.303 (sec). Leaf size: 64
dsolve((1-x^2)*diff(y(x),x$2)+(alpha-beta+(alpha+beta-2)*x)*diff(y(x),x)+(n+1)*(n+alpha+beta)*y(x)=0,y(x), singsol=all)
✓ Solution by Mathematica
Time used: 0.160 (sec). Leaf size: 74
DSolve[(1-x^2)*D[y[x],{x,2}]+(\[Alpha]-\[Beta]+(\[Alpha]+\[Beta]-2)*x)*D[y[x],x]+(n+1)*(n+\[Alpha]+\[Beta])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]