59.1.117 problem 119

Internal problem ID [9289]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 119
Date solved : Sunday, March 30, 2025 at 02:31:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 22

ode:=8*x^2*(-x^2+2)*diff(diff(y(x),x),x)+2*x*(-21*x^2+10)*diff(y(x),x)-(35*x^2+2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \,x^{{3}/{4}}+c_1}{\left (x^{2}-2\right ) \sqrt {x}} \]

✓ Mathematica. Time used: 0.27 (sec). Leaf size: 62

ode=8*x^2*(2-x^2)*D[y[x],{x,2}]+2*x*(10-21*x^2)*D[y[x],x]-(2+35*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} \sqrt [8]{x} \left (4 c_2 x^{3/4}+3 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {4 K[1]}{K[1]^2-2}+\frac {5}{4 K[1]}\right )dK[1]\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x**2*(2 - x**2)*Derivative(y(x), (x, 2)) + 2*x*(10 - 21*x**2)*Derivative(y(x), x) - (35*x**2 + 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False