23.3.402 problem 406

Internal problem ID [6116]
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 : 406
Date solved : Tuesday, September 30, 2025 at 02:21:46 PM
CAS classification : [_Jacobi]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 31

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x)*Derivative(y(x), (x, 2)) - (2 - 4*x)*Derivative(y(x), x) - 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False