23.3.395 problem 399

Internal problem ID [6109]
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 : 399
Date solved : Tuesday, September 30, 2025 at 02:21:40 PM
CAS classification : [_Jacobi]

\begin{align*} 6 y+\left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 51

ode:=6*y(x)+(1-2*x)*diff(y(x),x)+(1-x)*x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -6 c_2 \left (x^{2}-x +\frac {1}{6}\right ) \ln \left (-1+x \right )+6 c_2 \left (x^{2}-x +\frac {1}{6}\right ) \ln \left (x \right )+\left (-6 x +3\right ) c_2 +6 \left (x^{2}-x +\frac {1}{6}\right ) c_1 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 56

ode=6*y[x] + (1 - 2*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_1 \left (6 x^2-6 x+1\right )+c_2 \left (-\frac {1}{2} \left (6 x^2-6 x+1\right ) (\log (2-2 x)-\log (2 x))-3 x+\frac {3}{2}\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x)*Derivative(y(x), (x, 2)) + (1 - 2*x)*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False