59.1.672 problem 689

Internal problem ID [9844]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 689
Date solved : Sunday, March 30, 2025 at 02:47:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 23

ode:=4*x^2*diff(diff(y(x),x),x)+4*x*(1-x)*diff(y(x),x)+(2*x-9)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,{\mathrm e}^{x}+c_2 \left (x^{2}+2 x +2\right )}{x^{{3}/{2}}} \]

✓ Mathematica. Time used: 0.231 (sec). Leaf size: 38

ode=4*x^2*D[y[x],{x,2}]+4*x*(1-x)*D[y[x],x]+(2*x-9)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) + 4*x*(1 - x)*Derivative(y(x), x) + (2*x - 9)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False