60.3.102 problem 1116

Internal problem ID [11098]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1116
Date solved : Thursday, March 13, 2025 at 08:24:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.099 (sec). Leaf size: 31

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

\[ y = {\mathrm e}^{-a x} \left (\operatorname {KummerM}\left (b , b +n , a x \right ) c_{1} +\operatorname {KummerU}\left (b , b +n , a x \right ) c_{2} \right ) \]

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 38

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

\[ y(x)\to e^{-a x} (c_1 \operatorname {HypergeometricU}(b,b+n,a x)+c_2 L_{-b}^{b+n-1}(a x)) \]

✗ Sympy

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

ValueError : Expected Expr or iterable but got None