59.1.584 problem 600

Internal problem ID [9756]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 600
Date solved : Wednesday, March 05, 2025 at 07:58:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.044 (sec). Leaf size: 55

ode:=2*x^2*(x+2)*diff(diff(y(x),x),x)-x*(4-7*x)*diff(y(x),x)-(5-3*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {15 \,\operatorname {arctanh}\left (\frac {\sqrt {2}\, \sqrt {x +2}}{2}\right ) c_{2} x^{3}+33 c_{2} \sqrt {2}\, \left (x^{2}+\frac {52}{33} x +\frac {32}{33}\right ) \sqrt {x +2}+c_{1} x^{3}}{\sqrt {x}\, \left (x +2\right )^{{7}/{2}}} \]

✓ Mathematica. Time used: 0.257 (sec). Leaf size: 106

ode=2*x^2*(2+x)*D[y[x],{x,2}]-x*(4-7*x)*D[y[x],x]-(5-3*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {2}{K[1]}-\frac {5}{4 (K[1]+2)}\right )dK[1]-\frac {1}{2} \int _1^x\left (\frac {9}{2 (K[2]+2)}-\frac {1}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {3 K[1]+16}{4 K[1]^2+8 K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*(x + 2)*Derivative(y(x), (x, 2)) - x*(4 - 7*x)*Derivative(y(x), x) - (5 - 3*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False