59.1.513 problem 529

Internal problem ID [9685]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 529
Date solved : Sunday, March 30, 2025 at 02:44:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (4+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 27

ode:=x^2*(x+4)*diff(diff(y(x),x),x)-x*(1-3*x)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{{1}/{4}}}{\left (4+x \right )^{{9}/{4}}}+c_2 \operatorname {hypergeom}\left (\left [1, 3\right ], \left [\frac {7}{4}\right ], -\frac {x}{4}\right ) x \]

✓ Mathematica. Time used: 0.208 (sec). Leaf size: 109

ode=x^2*(4+x)*D[y[x],{x,2}]-x*(1-3*x)*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {1-K[1]}{2 K[1]^2+8 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {3 K[2]-1}{K[2] (K[2]+4)}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {1-K[1]}{2 K[1]^2+8 K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(x + 4)*Derivative(y(x), (x, 2)) - x*(1 - 3*x)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False