54.3.300 problem 1317

Internal problem ID [12595]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1317
Date solved : Friday, October 03, 2025 at 03:41:11 AM
CAS classification : [[_elliptic, _class_I]]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 13

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

\[ y = c_1 \operatorname {EllipticK}\left (x \right )+c_2 \operatorname {EllipticCK}\left (x \right ) \]

✓ Mathematica. Time used: 0.344 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to c_2 G_{2,2}^{2,0}\left (x^2| \begin {array}{c} \frac {1}{2},\frac {1}{2} \\ 0,0 \\ \end {array} \right )+\frac {2 c_1 \operatorname {EllipticK}\left (x^2\right )}{\pi } \end{align*}

✗ Sympy

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

False