59.1.604 problem 620

Internal problem ID [9776]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 620
Date solved : Wednesday, March 05, 2025 at 07:58:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 23

ode:=x^2*diff(diff(y(x),x),x)+x*(2*x^2+1)*diff(y(x),x)-(-10*x^2+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x \,{\mathrm e}^{-x^{2}} \left (x^{2}-2\right ) \left (c_{1} -2 c_{2} \right )}{2} \]

✓ Mathematica. Time used: 0.225 (sec). Leaf size: 51

ode=x^2*D[y[x],{x,2}]+x*(1+2*x^2)*D[y[x],x]-(1-10*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(2*x**2 + 1)*Derivative(y(x), x) - (1 - 10*x**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False