53.1.747 problem 769

Internal problem ID [11219]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 769
Date solved : Tuesday, September 30, 2025 at 07:37:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \end{align*}

✓ Maple. Time used: 0.082 (sec). Leaf size: 29

ode:=x^2*diff(diff(y(x),x),x)+(5/3*x+x^2)*diff(y(x),x)-1/3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-x} c_1 \,x^{{4}/{3}} \operatorname {hypergeom}\left (\left [2\right ], \left [\frac {7}{3}\right ], x\right )-3 c_2 x +c_2}{x} \]

✓ Mathematica. Time used: 0.167 (sec). Leaf size: 52

ode=x^2*D[y[x],{x,2}]+(5/3*x+x^2)*D[y[x],x]-1/3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {(3 x-1) \left (c_2 \int _1^x\frac {9 e^{-K[1]} \sqrt [3]{K[1]}}{(1-3 K[1])^2}dK[1]+c_1\right )}{3 x} \end{align*}

✓ Sympy. Time used: 0.808 (sec). Leaf size: 544

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + (x**2 + 5*x/3)*Derivative(y(x), x) - y(x)/3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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