59.1.63 problem 65

Internal problem ID [9235]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 65
Date solved : Wednesday, March 05, 2025 at 07:38:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y&=0 \end{align*}

✓ Maple. Time used: 0.168 (sec). Leaf size: 28

ode:=(x^3+1)*diff(diff(y(x),x),x)+7*x^2*diff(y(x),x)+9*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} \operatorname {hypergeom}\left (\left [1, 1\right ], \left [\frac {2}{3}\right ], -x^{3}\right )+\frac {c_{2} x}{\left (x^{3}+1\right )^{{4}/{3}}} \]

✓ Mathematica. Time used: 0.638 (sec). Leaf size: 39

ode=(1+x^3)*D[y[x],{x,2}]+7*x^2*D[y[x],x]+9*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1 x-c_2 \operatorname {Hypergeometric2F1}\left (-\frac {1}{3},-\frac {1}{3},\frac {2}{3},-x^3\right )}{\left (x^3+1\right )^{4/3}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(7*x**2*Derivative(y(x), x) + 9*x*y(x) + (x**3 + 1)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False