60.3.110 problem 1124

Internal problem ID [11106]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1124
Date solved : Sunday, March 30, 2025 at 07:42:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.042 (sec). Leaf size: 29

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

\[ y = c_1 \operatorname {KummerM}\left (-\frac {n}{2}, \frac {1}{2}+a , x^{2}\right )+c_2 \operatorname {KummerU}\left (-\frac {n}{2}, \frac {1}{2}+a , x^{2}\right ) \]

✓ Mathematica. Time used: 0.124 (sec). Leaf size: 65

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

\[ y(x)\to c_1 \operatorname {Hypergeometric1F1}\left (-\frac {n}{2},a+\frac {1}{2},x^2\right )+i^{1-2 a} c_2 x^{1-2 a} \operatorname {Hypergeometric1F1}\left (-a-\frac {n}{2}+\frac {1}{2},\frac {3}{2}-a,x^2\right ) \]

✗ Sympy

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

ValueError : Expected Expr or iterable but got None