59.1.657 problem 674

Internal problem ID [9829]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 674
Date solved : Wednesday, March 05, 2025 at 07:59:39 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

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

\[ y = \left (\operatorname {Ei}_{1}\left (-x \right ) c_{2} +c_{1} \right ) \sqrt {x} \]

✓ Mathematica. Time used: 0.206 (sec). Leaf size: 33

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

\[ y(x)\to \sqrt {x} \left (c_2 \int _1^x\frac {e^{K[1]}}{K[1]}dK[1]+c_1\right ) \]

✗ Sympy

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

False