23.3.386 problem 390

Internal problem ID [6100]
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 : 390
Date solved : Tuesday, September 30, 2025 at 02:21:32 PM
CAS classification : [_Jacobi]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 64

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

\[ y = \frac {12 c_2 \,x^{3} \left (-1+x \right ) \ln \left (-1+x \right )-12 c_2 \,x^{3} \left (-1+x \right ) \ln \left (x \right )+c_1 \,x^{4}+\left (-c_1 +12 c_2 \right ) x^{3}-6 c_2 \,x^{2}-2 c_2 x -c_2}{-1+x} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 62

ode=6*y[x] - 2*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 x^3-\frac {c_2 \left (12 x^3+12 (x-1) x^3 \log (1-x)-12 (x-1) x^3 \log (x)-6 x^2-2 x-1\right )}{3 (x-1)} \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE x**2*Derivative(y(x), (x, 2))/2 - x*Derivative(y(x), (x, 2))/2 -