23.3.460 problem 465

Internal problem ID [6174]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 465
Date solved : Tuesday, September 30, 2025 at 02:24:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -a \left (2+a \right ) y+4 a x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=-a*(2+a)*y(x)+4*a*x*diff(y(x),x)+4*(-x^2+1)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (x -1\right )^{1+\frac {a}{2}}+c_2 \left (x +1\right )^{1+\frac {a}{2}} \]

✓ Mathematica. Time used: 6.769 (sec). Leaf size: 103

ode=-(a*(2 + a)*y[x]) + 4*a*x*D[y[x],x] + 4*(1 - x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\left (1-x^2\right )^{\frac {1}{2}-\frac {1}{4} \sqrt {(a+2)^2}} \left (x^2-1\right )^{a/4} \left (\sqrt {(a+2)^2} c_1 (1-x)^{\frac {1}{2} \sqrt {(a+2)^2}}+c_2 (x+1)^{\frac {1}{2} \sqrt {(a+2)^2}}\right )}{\sqrt {(a+2)^2}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(4*a*x*Derivative(y(x), x) - a*(a + 2)*y(x) + (4 - 4*x**2)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False