59.1.295 problem 298

Internal problem ID [9467]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 298
Date solved : Sunday, March 30, 2025 at 02:35:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 14

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

\[ y = \left (x +1\right ) \left (c_2 \ln \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.25 (sec). Leaf size: 45

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

\[ y(x)\to \sqrt {x} (c_2 \log (x)+c_1) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {1}{K[1]}-\frac {2}{K[1]+1}\right )dK[1]\right ) \]

✗ Sympy

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

False