61.28.10 problem 70

Internal problem ID [12491]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-3
Problem number : 70
Date solved : Thursday, March 13, 2025 at 11:42:53 PM
CAS classification : [_Laguerre]

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

✓ Maple. Time used: 0.146 (sec). Leaf size: 17

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

\[ y = c_{1} \operatorname {KummerM}\left (a , b , x\right )+c_{2} \operatorname {KummerU}\left (a , b , x\right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 24

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

\[ y(x)\to c_1 \operatorname {HypergeometricU}(a,b,x)+c_2 L_{-a}^{b-1}(x) \]

✗ Sympy

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

ValueError : Expected Expr or iterable but got None