59.1.230 problem 233

Internal problem ID [9402]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 233
Date solved : Sunday, March 30, 2025 at 02:34:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.097 (sec). Leaf size: 38

ode:=3*x^2*diff(diff(y(x),x),x)-x*(x+8)*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \left (x^{{2}/{3}}-\frac {x^{{5}/{3}}}{2}+\frac {x^{{8}/{3}}}{4}\right ) {\mathrm e}^{\frac {x}{3}}+c_1 \,x^{3} \operatorname {hypergeom}\left (\left [3\right ], \left [\frac {10}{3}\right ], \frac {x}{3}\right ) \]

✓ Mathematica. Time used: 0.818 (sec). Leaf size: 99

ode=3*x^2*D[y[x],{x,2}]-x*(x+8)*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^{4/3} \left (x^2-2 x+4\right ) \exp \left (\frac {1}{6} \left (6 \int _1^x\frac {K[1]-4}{6 K[1]}dK[1]+x+8\right )\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[2]}\frac {K[1]-4}{6 K[1]}dK[1]\right )}{\left (K[2]^2-2 K[2]+4\right )^2}dK[2]+c_1\right ) \]

✓ Sympy. Time used: 1.370 (sec). Leaf size: 474

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*Derivative(y(x), (x, 2)) - x*(x + 8)*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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