60.3.298 problem 1315

Internal problem ID [11294]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1315
Date solved : Sunday, March 30, 2025 at 08:08:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=x*(x^2-1)*diff(diff(y(x),x),x)+diff(y(x),x)+y(x)*a*x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (\sqrt {a}\, \sqrt {x^{2}-1}\right )+c_2 \cos \left (\sqrt {a}\, \sqrt {x^{2}-1}\right ) \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 44

ode=a*x^3*y[x] + D[y[x],x] + x*(-1 + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \cos \left (\sqrt {a} \sqrt {x^2-1}\right )+c_2 \sin \left (\sqrt {a} \sqrt {x^2-1}\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*x**3*y(x) + x*(x**2 - 1)*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False