82.48.2 problem Ex. 2

Internal problem ID [18912]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 2
Date solved : Monday, March 31, 2025 at 06:24:23 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(diff(y(x),x),x)-a^2/x/(a^2-x^2)*diff(y(x),x) = x^2/a/(a^2-x^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 c_1 a \sqrt {a +x}\, \sqrt {x -a}+2 c_2 a -x^{2}}{2 a} \]

✓ Mathematica. Time used: 0.096 (sec). Leaf size: 36

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

\[ y(x)\to c_2-\frac {\left (\sqrt {x^2-a^2}-a c_1\right ){}^2}{2 a} \]

✗ Sympy

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

Timed Out