54.3.82 problem 1096

Internal problem ID [12377]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1096
Date solved : Friday, October 03, 2025 at 03:18:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+y^{\prime }+\left (x +a \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 34

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

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 55

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

\begin{align*} y(x)&\to e^{-i x} \left (c_1 \operatorname {HypergeometricU}\left (\frac {i a}{2}+\frac {1}{2},1,2 i x\right )+c_2 \operatorname {LaguerreL}\left (-\frac {1}{2} i (a-i),2 i x\right )\right ) \end{align*}

✗ Sympy

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

False