59.1.580 problem 596

Internal problem ID [9752]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 596
Date solved : Sunday, March 30, 2025 at 02:45:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

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

\[ y = \frac {x \left (\ln \left (x \right ) c_2 +c_1 \right )}{4+3 x} \]

✓ Mathematica. Time used: 0.254 (sec). Leaf size: 49

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

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

✗ Sympy

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

False