83.30.13 problem 13

Internal problem ID [19321]
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 : 13
Date solved : Monday, March 31, 2025 at 07:06:50 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 31

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

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

✗ 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,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out