54.3.124 problem 1138

Internal problem ID [12419]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1138
Date solved : Friday, October 03, 2025 at 03:19:04 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x y^{\prime \prime }+4 m y^{\prime }-\left (x -2 m -4 n \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 26

ode:=4*x*diff(diff(y(x),x),x)+4*m*diff(y(x),x)-(x-2*m-4*n)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 32

ode=(2*m + 4*n - x)*y[x] + 4*m*D[y[x],x] + 4*x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x/2} (c_1 \operatorname {HypergeometricU}(-n,m,x)+c_2 L_n^{m-1}(x)) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
m = symbols("m") 
n = symbols("n") 
y = Function("y") 
ode = Eq(4*m*Derivative(y(x), x) + 4*x*Derivative(y(x), (x, 2)) - (-2*m - 4*n + x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None