59.1.241 problem 244

Internal problem ID [9413]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 244
Date solved : Wednesday, March 05, 2025 at 07:48:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 35

ode:=x^2*diff(diff(y(x),x),x)+x*(x^2+6)*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_{2} {\mathrm e}^{-\frac {x^{2}}{2}} \operatorname {hypergeom}\left (\left [2\right ], \left [\frac {1}{2}\right ], \frac {x^{2}}{2}\right )+c_{1} \left (x^{2}+3\right ) x}{x^{3}} \]

✓ Mathematica. Time used: 0.596 (sec). Leaf size: 50

ode=x^2*D[y[x],{x,2}]+x*(6+x^2)*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 2.635 (sec). Leaf size: 882

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(x**2 + 6)*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]