59.1.89 problem 91

Internal problem ID [9261]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 91
Date solved : Wednesday, March 05, 2025 at 07:46:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.085 (sec). Leaf size: 30

ode:=3*x^2*diff(diff(y(x),x),x)+x*(1+x)*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 56

ode=3*x^2*D[y[x],{x,2}]+x*(1+x)*D[y[x],x]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{\frac {1}{3} (-x-1)} \left (c_2 x^{2/3}-3 \sqrt [3]{3 e} c_1 (-x)^{2/3} \Gamma \left (\frac {4}{3},-\frac {x}{3}\right )\right )}{x} \]

✓ Sympy. Time used: 1.438 (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 + 1)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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