60.3.78 problem 1092

Internal problem ID [11074]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1092
Date solved : Thursday, March 13, 2025 at 08:24:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 25

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

\[ y = c_{1} \operatorname {WhittakerM}\left (-\frac {i a}{2}, \frac {1}{2}, 2 i x \right )+c_{2} \operatorname {WhittakerW}\left (-\frac {i a}{2}, \frac {1}{2}, 2 i x \right ) \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 53

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

\[ y(x)\to e^{-i x} x \left (c_2 \operatorname {Hypergeometric1F1}\left (\frac {i a}{2}+1,2,2 i x\right )+c_1 \operatorname {HypergeometricU}\left (\frac {i a}{2}+1,2,2 i x\right )\right ) \]

✗ 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),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False