54.3.118 problem 1132

Internal problem ID [12413]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1132
Date solved : Friday, October 03, 2025 at 03:19:02 AM
CAS classification : [_Laguerre]

\begin{align*} 2 x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+a y&=0 \end{align*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 29

ode:=2*x*diff(diff(y(x),x),x)-(2*x-1)*diff(y(x),x)+a*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 44

ode=a*y[x] - (-1 + 2*x)*D[y[x],x] + 2*x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {x} \left (c_1 \operatorname {HypergeometricU}\left (\frac {1-a}{2},\frac {3}{2},x\right )+c_2 L_{\frac {a-1}{2}}^{\frac {1}{2}}(x)\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, 2)) - (2*x - 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False