59.1.597 problem 613

Internal problem ID [9769]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 613
Date solved : Sunday, March 30, 2025 at 02:46:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 82

ode:=x^2*(1+x)*diff(diff(y(x),x),x)+x*(1-10*x)*diff(y(x),x)-(9-10*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {8 c_2 \,x^{13}+91 c_2 \,x^{12}+468 c_2 \,x^{11}+1430 c_2 \,x^{10}+2860 c_2 \,x^{9}+3861 c_2 \,x^{8}+3432 c_2 \,x^{7}+1716 c_2 \,x^{6}+715 c_1 \,x^{4}+572 c_1 \,x^{3}+234 c_1 \,x^{2}+52 c_1 x +5 c_1}{x^{3}} \]

✓ Mathematica. Time used: 0.472 (sec). Leaf size: 123

ode=x^2*(1+x)*D[y[x],{x,2}]+x*(1-10*x)*D[y[x],x]-(9-10*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{8} (8 x-5) \exp \left (\int _1^x\frac {8 K[1]-5}{2 K[1] (K[1]+1)}dK[1]-\frac {1}{2} \int _1^x\left (\frac {1}{K[2]}-\frac {11}{K[2]+1}\right )dK[2]\right ) \left (c_2 \int _1^x\frac {64 \exp \left (-2 \int _1^{K[3]}\frac {8 K[1]-5}{2 K[1] (K[1]+1)}dK[1]\right )}{(5-8 K[3])^2}dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(x + 1)*Derivative(y(x), (x, 2)) + x*(1 - 10*x)*Derivative(y(x), x) - (9 - 10*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False