59.1.675 problem 692

Internal problem ID [9847]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 692
Date solved : Sunday, March 30, 2025 at 02:48:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1+2 x \right ) y^{\prime }+\left (4 x -1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 16

ode:=4*x^2*diff(diff(y(x),x),x)+4*x*(2*x+1)*diff(y(x),x)+(4*x-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \,{\mathrm e}^{-2 x}+c_1}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 26

ode=4*x^2*D[y[x],{x,2}]+4*x*(1+2*x)*D[y[x],x]+(4*x-1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 c_1 e^{-2 x}+c_2}{2 \sqrt {x}} \]

✗ Sympy

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

False