59.1.769 problem 791

Internal problem ID [9941]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 791
Date solved : Wednesday, March 05, 2025 at 08:01:13 AM
CAS classification : [_Jacobi]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 14

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

\[ y = c_{2} \sqrt {x}+c_{1} x +c_{1} \]

✓ Mathematica. Time used: 0.252 (sec). Leaf size: 106

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

\[ y(x)\to \exp \left (\int _1^x\frac {K[1]-3}{4 (K[1]-1) K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {K[2]+1}{2 K[2]-2 K[2]^2}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]-3}{4 (K[1]-1) K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

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

False