59.1.549 problem 565

Internal problem ID [9721]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 565
Date solved : Sunday, March 30, 2025 at 02:45:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.148 (sec). Leaf size: 32

ode:=16*x^2*diff(diff(y(x),x),x)+4*x*(2*x^2+x+6)*diff(y(x),x)+(18*x^2+5*x+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-\frac {x \left (x +1\right )}{4}} \left (\int \frac {{\mathrm e}^{\frac {x \left (x +1\right )}{4}}}{x}d x c_2 +c_1 \right )}{x^{{1}/{4}}} \]

✓ Mathematica. Time used: 0.413 (sec). Leaf size: 57

ode=16*x^2*D[y[x],{x,2}]+4*x*(6+x+2*x^2)*D[y[x],x]+(1+5*x+18*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*x**2*Derivative(y(x), (x, 2)) + 4*x*(2*x**2 + x + 6)*Derivative(y(x), x) + (18*x**2 + 5*x + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False