60.3.265 problem 1281

Internal problem ID [11261]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1281
Date solved : Sunday, March 30, 2025 at 08:04:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 15

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

\[ y = \frac {{\mathrm e}^{x} \left (c_2 x +c_1 \right )}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 21

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

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

✗ 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**2 - 4*x - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False