54.3.41 problem 1046

Internal problem ID [12336]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1046
Date solved : Friday, October 03, 2025 at 03:18:27 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 x y^{\prime }+a y&=0 \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 31

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

\[ y = x \left (\operatorname {KummerM}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) c_1 +\operatorname {KummerU}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) c_2 \right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 31

ode=a*y[x] - 2*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 (\frac {a}{2},x\right )+c_2 \operatorname {Hypergeometric1F1}\left (-\frac {a}{4},\frac {1}{2},x^2\right ) \end{align*}

✗ Sympy

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

False