59.1.694 problem 711

Internal problem ID [9866]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 711
Date solved : Sunday, March 30, 2025 at 02:48:25 PM
CAS classification : [_Jacobi]

\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 29

ode:=2*x*(1-x)*diff(diff(y(x),x),x)+(1-11*x)*diff(y(x),x)-10*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \left (x^{2}+6 x +1\right )+c_2 \sqrt {x}\, \left (x +1\right )}{\left (-1+x \right )^{4}} \]

✓ Mathematica. Time used: 0.534 (sec). Leaf size: 119

ode=2*x*(1-x)*D[y[x],{x,2}]+(1-11*x)*D[y[x],x]-10*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*(1 - x)*Derivative(y(x), (x, 2)) + (1 - 11*x)*Derivative(y(x), x) - 10*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False