54.3.39 problem 1044

Internal problem ID [12334]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1044
Date solved : Friday, October 03, 2025 at 03:18:26 AM
CAS classification : [_Hermite]

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 39

ode=-(a*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 c_1 \operatorname {HermiteH}\left (-a,\frac {x}{\sqrt {2}}\right )+c_2 \operatorname {Hypergeometric1F1}\left (\frac {a}{2},\frac {1}{2},\frac {x^2}{2}\right ) \end{align*}

✗ Sympy

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

False