59.1.571 problem 587

Internal problem ID [9743]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 587
Date solved : Wednesday, March 05, 2025 at 07:58:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 47

ode:=x^2*(1-x)*diff(diff(y(x),x),x)-x*(3-5*x)*diff(y(x),x)+(4-5*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2} \left (c_{1} \left (x -1\right )^{3}+c_{2} \left (-\left (x -1\right )^{3} \ln \left (x -1\right )+\left (x -1\right )^{3} \ln \left (x \right )-x^{2}+\frac {5 x}{2}-\frac {11}{6}\right )\right ) \]

✓ Mathematica. Time used: 0.244 (sec). Leaf size: 104

ode=x^2*(1-x)*D[y[x],{x,2}]-x*(3-5*x)*D[y[x],x]+(4-5*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(1 - x)*Derivative(y(x), (x, 2)) - x*(3 - 5*x)*Derivative(y(x), x) + (4 - 5*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False