23.3.461 problem 466

Internal problem ID [6175]
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 : 466
Date solved : Friday, October 03, 2025 at 01:48:06 AM
CAS classification : [_Jacobi]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 56

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

\[ y = \left (1-x \right ) \left (c_1 \operatorname {hypergeom}\left (\left [\frac {3}{4}+\frac {\sqrt {5}}{4}, \frac {3}{4}-\frac {\sqrt {5}}{4}\right ], \left [\frac {1}{2}\right ], x\right )+c_2 \sqrt {x}\, \operatorname {hypergeom}\left (\left [\frac {5}{4}+\frac {\sqrt {5}}{4}, \frac {5}{4}-\frac {\sqrt {5}}{4}\right ], \left [\frac {3}{2}\right ], x\right )\right ) \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 78

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

\begin{align*} y(x)&\to c_1 \operatorname {Hypergeometric2F1}\left (\frac {1}{4} \left (-1-\sqrt {5}\right ),\frac {1}{4} \left (-1+\sqrt {5}\right ),\frac {1}{2},x\right )+i c_2 \sqrt {x} \operatorname {Hypergeometric2F1}\left (\frac {1}{4} \left (1-\sqrt {5}\right ),\frac {1}{4} \left (1+\sqrt {5}\right ),\frac {3}{2},x\right ) \end{align*}

✗ Sympy

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

False