59.1.654 problem 671

Internal problem ID [9826]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 671
Date solved : Sunday, March 30, 2025 at 02:47:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 40

ode:=6*x^2*diff(diff(y(x),x),x)+x*(1+18*x)*diff(y(x),x)+(1+12*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\frac {c_2 \left (-x \right )^{{5}/{6}} 3^{{5}/{6}}}{3}+x \,{\mathrm e}^{-3 x} \left (c_2 \Gamma \left (\frac {5}{6}\right )-c_2 \Gamma \left (\frac {5}{6}, -3 x \right )+c_1 \right )}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 47

ode=6*x^2*D[y[x],{x,2}]+x*(1+18*x)*D[y[x],x]+(1+12*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (\frac {\sqrt [6]{3} c_2 x^{4/3} \Gamma \left (-\frac {1}{6},-3 x\right )}{(-x)^{5/6}}+c_1 \sqrt {x}\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x**2*Derivative(y(x), (x, 2)) + x*(18*x + 1)*Derivative(y(x), x) + (12*x + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False