23.3.397 problem 401

Internal problem ID [6111]
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 : 401
Date solved : Friday, October 03, 2025 at 01:46:26 AM
CAS classification : [_Jacobi]

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 79

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

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

✓ Mathematica. Time used: 0.464 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to c_2 G_{2,2}^{2,0}\left (x\left | \begin {array}{c} 1-\sqrt {2},1+\sqrt {2} \\ 0,0 \\ \end {array} \right .\right )+c_1 \operatorname {Hypergeometric2F1}\left (-\sqrt {2},\sqrt {2},1,x\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x)*Derivative(y(x), (x, 2)) + (1 - x)*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False