59.1.715 problem 732

Internal problem ID [9887]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 732
Date solved : Wednesday, March 05, 2025 at 08:00:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.163 (sec). Leaf size: 100

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

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

✗ Sympy

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

False