59.1.567 problem 583

Internal problem ID [9739]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 583
Date solved : Sunday, March 30, 2025 at 02:45:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 25

ode:=9*x^2*diff(diff(y(x),x),x)-3*x*(-2*x^2+7)*diff(y(x),x)+(2*x^2+25)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 39

ode=9*x^2*D[y[x],{x,2}]-3*x*(7-2*x^2)*D[y[x],x]+(25+2*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} e^{-\frac {x^2}{3}} x^{5/3} \left (c_2 \operatorname {ExpIntegralEi}\left (\frac {x^2}{3}\right )+2 c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2*Derivative(y(x), (x, 2)) - 3*x*(7 - 2*x**2)*Derivative(y(x), x) + (2*x**2 + 25)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False