54.3.117 problem 1131

Internal problem ID [12412]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1131
Date solved : Friday, October 03, 2025 at 03:19:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 48

ode=a*y[x] - (-1 + 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}{2}-a,\frac {3}{2},\frac {x}{2}\right )+c_2 L_{a-\frac {1}{2}}^{\frac {1}{2}}\left (\frac {x}{2}\right )\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)) - (x - 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False