6.8.18 problem 21

Internal problem ID [1754]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 21
Date solved : Tuesday, September 30, 2025 at 05:19:03 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=(x^2-4)*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 x +c_2}{x^{2}-4} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to \frac {c_2 x+c_1}{x^2-4} \end{align*}

✗ Sympy

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

False