59.1.101 problem 103

Internal problem ID [9273]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 103
Date solved : Sunday, March 30, 2025 at 02:31:13 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 32

ode:=x*(x^2+3)*diff(diff(y(x),x),x)+(-x^2+2)*diff(y(x),x)-8*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{{1}/{3}} \left (x^{2}+3\right )^{{11}/{6}}+\frac {c_2 \left (8 x^{4}+44 x^{2}+55\right )}{8} \]

✓ Mathematica. Time used: 0.227 (sec). Leaf size: 116

ode=x*(3+x^2)*D[y[x],{x,2}]+(2-x^2)*D[y[x],x]-8*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {7 K[1]^2+4}{2 K[1]^3+6 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {2-K[2]^2}{K[2]^3+3 K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {7 K[1]^2+4}{2 K[1]^3+6 K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**2 + 3)*Derivative(y(x), (x, 2)) - 8*x*y(x) + (2 - x**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False