59.1.436 problem 449

Internal problem ID [9608]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 449
Date solved : Wednesday, March 05, 2025 at 07:51:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

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

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

\[ y = \frac {{\mathrm e}^{x} \left (c_{2} x^{2}+c_{1} \right )}{x} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 23

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

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

✗ Sympy

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

False