59.1.791 problem 813

Internal problem ID [9963]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 813
Date solved : Wednesday, March 05, 2025 at 08:01:30 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

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

\[ y = \frac {\left (x^{3}+3 x^{2}+3 x \right ) c_{2} +c_{1}}{x \left (x +1\right )} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 34

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

\[ y(x)\to \frac {c_2 x \left (x^2+3 x+3\right )+3 c_1}{3 x (x+1)} \]

✗ Sympy

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

False