59.1.92 problem 94

Internal problem ID [9264]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 94
Date solved : Sunday, March 30, 2025 at 02:31:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} \left (3+x \right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (1+x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 36

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

\[ y = c_1 \sqrt {x}\, \operatorname {hypergeom}\left (\left [1, \frac {3}{2}\right ], \left [\frac {7}{6}\right ], -\frac {x}{3}\right )+\frac {c_2 \,x^{{1}/{3}}}{\left (3+x \right ) \left (1+\frac {x}{3}\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.256 (sec). Leaf size: 108

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

\[ y(x)\to \exp \left (\int _1^x\frac {K[1]+5}{4 K[1]^2+12 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {5 K[2]+1}{2 K[2]^2+6 K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]+5}{4 K[1]^2+12 K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*(x + 3)*Derivative(y(x), (x, 2)) + x*(5*x + 1)*Derivative(y(x), x) + (x + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False