59.1.530 problem 546

Internal problem ID [9702]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 546
Date solved : Wednesday, March 05, 2025 at 07:57:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.087 (sec). Leaf size: 36

ode:=6*x^2*diff(diff(y(x),x),x)+x*(6*x^2+1)*diff(y(x),x)+(9*x^2+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-\frac {x^{2}}{4}} \left ({\mathrm e}^{-\frac {x^{2}}{4}} x^{{11}/{12}} c_{2} +\operatorname {WhittakerM}\left (\frac {11}{24}, \frac {1}{24}, \frac {x^{2}}{2}\right ) c_{1} \right )}{x^{{7}/{12}}} \]

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 61

ode=6*x^2*D[y[x],{x,2}]+x*(1+6*x^2)*D[y[x],x]+(1+9*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{-\frac {x^2}{2}} \left (2 c_1 x^{11/6}+\sqrt [12]{2} c_2 \left (-x^2\right )^{11/12} \Gamma \left (\frac {1}{12},-\frac {x^2}{2}\right )\right )}{2 x^{3/2}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x**2*Derivative(y(x), (x, 2)) + x*(6*x**2 + 1)*Derivative(y(x), x) + (9*x**2 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False