54.3.120 problem 1134

Internal problem ID [12415]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1134
Date solved : Friday, October 03, 2025 at 03:19:03 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x y^{\prime \prime }-\left (x +a \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 21

ode:=4*x*diff(diff(y(x),x),x)-(x+a)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {WhittakerM}\left (-\frac {a}{4}, \frac {1}{2}, x\right )+c_2 \operatorname {WhittakerW}\left (-\frac {a}{4}, \frac {1}{2}, x\right ) \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 44

ode=(-a - x)*y[x] + 4*x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} e^{-x/2} x \left (c_2 \operatorname {Hypergeometric1F1}\left (\frac {a}{4}+1,2,x\right )+c_1 \operatorname {HypergeometricU}\left (\frac {a}{4}+1,2,x\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), (x, 2)) - (a + x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False