23.3.382 problem 386

Internal problem ID [6096]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 386
Date solved : Tuesday, September 30, 2025 at 02:21:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -12 y-8 x y^{\prime }+\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 41

ode:=-12*y(x)-8*x*diff(y(x),x)+(a^2-x^2)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 38

ode=-12*y[x] - 8*x*D[y[x],x] + (a^2 - x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\frac {c_2 \left (a^2+3 x^2\right )}{(a-x)^3}+3 c_1}{3 (a+x)^3} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-8*x*Derivative(y(x), x) + (a**2 - x**2)*Derivative(y(x), (x, 2)) - 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False