62.38.10 problem Ex 10

Internal problem ID [12942]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 62. Summary. Page 144
Problem number : Ex 10
Date solved : Wednesday, March 05, 2025 at 08:54:20 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=(-x^2+1)*diff(diff(y(x),x),x)-1/x*diff(y(x),x)+x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}}{2}+\sqrt {x -1}\, \sqrt {x +1}\, c_{1} +c_{2} \]

✓ Mathematica. Time used: 3.578 (sec). Leaf size: 84

ode=(1-x^2)*D[y[x],{x,2}]-1/x*D[y[x],x]+x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^x\exp \left (\int _1^{K[3]}\frac {1}{K[1]-K[1]^3}dK[1]\right ) \left (c_1+\int _1^{K[3]}\frac {\exp \left (-\int _1^{K[2]}\frac {1}{K[1]-K[1]^3}dK[1]\right ) K[2]^2}{K[2]^2-1}dK[2]\right )dK[3]+c_2 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 + (1 - x**2)*Derivative(y(x), (x, 2)) - Derivative(y(x), x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out