54.3.37 problem 1042

Internal problem ID [12332]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1042
Date solved : Friday, October 03, 2025 at 03:18:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+x y^{\prime }-n y&=0 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 41

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

\[ y = {\mathrm e}^{-\frac {x^{2}}{2}} x \left (\operatorname {KummerM}\left (1+\frac {n}{2}, \frac {3}{2}, \frac {x^{2}}{2}\right ) c_1 +\operatorname {KummerU}\left (1+\frac {n}{2}, \frac {3}{2}, \frac {x^{2}}{2}\right ) c_2 \right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to e^{-\frac {x^2}{2}} \left (c_1 \operatorname {HermiteH}\left (-n-1,\frac {x}{\sqrt {2}}\right )+c_2 \operatorname {Hypergeometric1F1}\left (\frac {n+1}{2},\frac {1}{2},\frac {x^2}{2}\right )\right ) \end{align*}

✗ Sympy

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

False