59.1.132 problem 134

Internal problem ID [9304]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 134
Date solved : Wednesday, March 05, 2025 at 07:47:13 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 30

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

\[ y = \frac {x^{2} \left (c_{2} \left (x -1\right ) \ln \left (x \right )+c_{1} x -c_{1} -4 c_{2} \right )}{\left (x +1\right )^{3}} \]

✓ Mathematica. Time used: 0.459 (sec). Leaf size: 111

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

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

✗ Sympy

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

False