59.1.115 problem 117

Internal problem ID [9287]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 117
Date solved : Sunday, March 30, 2025 at 02:31:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 24

ode:=6*x^2*(2*x^2+1)*diff(diff(y(x),x),x)+x*(50*x^2+1)*diff(y(x),x)+(30*x^2+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{{1}/{3}} \left (c_1 \,x^{{1}/{6}}+c_2 \right )}{2 x^{2}+1} \]

✓ Mathematica. Time used: 0.277 (sec). Leaf size: 58

ode=6*x^2*(1+2*x^2)*D[y[x],{x,2}]+x*(1+50*x^2)*D[y[x],x]+(1+30*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^{5/12} \left (6 c_2 \sqrt [6]{x}+c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\frac {50 K[1]^2+1}{12 K[1]^3+6 K[1]}dK[1]\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x**2*(2*x**2 + 1)*Derivative(y(x), (x, 2)) + x*(50*x**2 + 1)*Derivative(y(x), x) + (30*x**2 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False