23.3.514 problem 520

Internal problem ID [6228]
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 : 520
Date solved : Tuesday, September 30, 2025 at 02:36:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {-c_2 x^2-c_1 x+2 c_2 x \log (x)+c_2}{x-1} \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE x*(1 - x)**2*Derivative(y(x), (x, 2)) - 2*y(x) cannot be solved