59.1.159 problem 161

Internal problem ID [9331]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 161
Date solved : Sunday, March 30, 2025 at 02:32:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 21

ode:=16*x^2*(x^2+1)*diff(diff(y(x),x),x)+8*x*(9*x^2+1)*diff(y(x),x)+(49*x^2+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{{1}/{4}} \left (\ln \left (x \right ) c_2 +c_1 \right )}{x^{2}+1} \]

✓ Mathematica. Time used: 0.244 (sec). Leaf size: 53

ode=16*x^2*(1+x^2)*D[y[x],{x,2}]+8*x*(1+9*x^2)*D[y[x],x]+(1+49*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt {x} (c_2 \log (x)+c_1) \exp \left (-\frac {1}{2} \int _1^x\frac {9 K[1]^2+1}{2 \left (K[1]^3+K[1]\right )}dK[1]\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*x**2*(x**2 + 1)*Derivative(y(x), (x, 2)) + 8*x*(9*x**2 + 1)*Derivative(y(x), x) + (49*x**2 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False