83.30.6 problem 6

Internal problem ID [19306]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 6
Date solved : Thursday, March 13, 2025 at 02:12:50 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: 0.003 (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);
 

\[ y \left (x \right ) = \frac {2 c_{1} a \sqrt {-a +x}\, \sqrt {a +x}+2 c_{2} a -x^{2}}{2 a} \]

✓ Mathematica. Time used: 0.074 (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