59.1.301 problem 304

Internal problem ID [9473]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 304
Date solved : Sunday, March 30, 2025 at 02:35:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.183 (sec). Leaf size: 132

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

\[ y(x)\to c_2 x^{1+\sqrt {2}} \operatorname {Hypergeometric2F1}\left (-\frac {1}{2}+\sqrt {2}-\frac {\sqrt {17}}{2},-\frac {1}{2}+\sqrt {2}+\frac {\sqrt {17}}{2},1+2 \sqrt {2},-x\right )+c_1 x^{1-\sqrt {2}} \operatorname {Hypergeometric2F1}\left (\frac {1}{2} \left (-1-2 \sqrt {2}-\sqrt {17}\right ),\frac {1}{2} \left (-1-2 \sqrt {2}+\sqrt {17}\right ),1-2 \sqrt {2},-x\right ) \]

✗ Sympy

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

False