59.1.733 problem 750

Internal problem ID [9905]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 750
Date solved : Wednesday, March 05, 2025 at 08:00:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 18

ode:=x^2*(1-x)*diff(diff(y(x),x),x)+(5*x-4)*x*diff(y(x),x)+(6-9*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2} \left (\ln \left (x \right ) c_{2} x +c_{1} x +c_{2} \right ) \]

✓ Mathematica. Time used: 0.227 (sec). Leaf size: 98

ode=(1-x)*x^2*D[y[x],{x,2}]+(5*x-4)*x*D[y[x],x]+(6-9*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(1 - x)*Derivative(y(x), (x, 2)) + x*(5*x - 4)*Derivative(y(x), x) + (6 - 9*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False