59.1.95 problem 97

Internal problem ID [9267]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 97
Date solved : Sunday, March 30, 2025 at 02:31:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.079 (sec). Leaf size: 25

ode:=6*x^2*diff(diff(y(x),x),x)+x*(10-x)*diff(y(x),x)-(x+2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,{\mathrm e}^{\frac {x}{12}} \operatorname {WhittakerM}\left (-\frac {1}{6}, \frac {2}{3}, \frac {x}{6}\right )}{x^{{5}/{6}}}+\frac {c_2}{x} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 38

ode=6*x^2*D[y[x],{x,2}]+x*(10-x)*D[y[x],x]-(2+x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 \sqrt [3]{x} L_{-\frac {4}{3}}^{\frac {4}{3}}\left (\frac {x}{6}\right )+\frac {6 \sqrt [3]{6} c_1}{x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x**2*Derivative(y(x), (x, 2)) + x*(10 - x)*Derivative(y(x), x) - (x + 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False