59.1.587 problem 603

Internal problem ID [9759]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 603
Date solved : Sunday, March 30, 2025 at 02:46:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 35

ode:=x^2*(-2*x^2+1)*diff(diff(y(x),x),x)+x*(-13*x^2+7)*diff(y(x),x)-14*x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \left (2 x^{2}-1\right )^{{5}/{4}}+5 c_2 \,x^{4}-20 c_2 \,x^{2}+8 c_2}{x^{6}} \]

✓ Mathematica. Time used: 0.214 (sec). Leaf size: 116

ode=x^2*(1-2*x^2)*D[y[x],{x,2}]+x*(7-13*x^2)*D[y[x],x]-14*x^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {5-K[1]^2}{4 K[1]^3-2 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {7-13 K[2]^2}{K[2]-2 K[2]^3}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {5-K[1]^2}{4 K[1]^3-2 K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(1 - 2*x**2)*Derivative(y(x), (x, 2)) - 14*x**2*y(x) + x*(7 - 13*x**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False