53.1.658 problem 675

Internal problem ID [11130]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 675
Date solved : Tuesday, September 30, 2025 at 07:36:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

ode:=x^2*diff(diff(y(x),x),x)+x*(3-2*x)*diff(y(x),x)+(1-2*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 33

ode=x^2*D[y[x],{x,2}]+x*(3-2*x)*D[y[x],x]+(1-2*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 \int _1^x\frac {e^{2 K[1]}}{K[1]}dK[1]+c_1}{x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(3 - 2*x)*Derivative(y(x), x) + (1 - 2*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False