59.1.492 problem 508

Internal problem ID [9664]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 508
Date solved : Sunday, March 30, 2025 at 02:43:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.065 (sec). Leaf size: 31

ode:=(2*x^2+3*x)*diff(diff(y(x),x),x)+10*(1+x)*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \left (2+x \right )}{\left (1+\frac {2 x}{3}\right )^{{2}/{3}} x^{{7}/{3}}}+c_2 \operatorname {hypergeom}\left (\left [2, 2\right ], \left [\frac {10}{3}\right ], -\frac {2 x}{3}\right ) \]

✓ Mathematica. Time used: 0.424 (sec). Leaf size: 118

ode=(3*x+2*x^2)*D[y[x],{x,2}]+10*(1+x)*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (x+2) \exp \left (\int _1^x-\frac {K[1]+2}{2 K[1]^2+3 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {10 (K[2]+1)}{K[2] (2 K[2]+3)}dK[2]\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[3]}-\frac {K[1]+2}{2 K[1]^2+3 K[1]}dK[1]\right )}{(K[3]+2)^2}dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((10*x + 10)*Derivative(y(x), x) + (2*x**2 + 3*x)*Derivative(y(x), (x, 2)) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False