54.3.47 problem 1052

Internal problem ID [12342]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1052
Date solved : Friday, October 03, 2025 at 03:18:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 58

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

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 67

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

✗ Sympy

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

False