23.3.208 problem 210

Internal problem ID [5922]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 210
Date solved : Friday, October 03, 2025 at 01:45:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 30

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

\[ y = {\mathrm e}^{-x} \left (\operatorname {KummerM}\left (-b +a , a , x\right ) c_1 +\operatorname {KummerU}\left (-b +a , a , x\right ) c_2 \right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to e^{-x} (c_1 \operatorname {HypergeometricU}(a-b,a,x)+c_2 L_{b-a}^{a-1}(x)) \end{align*}

✗ Sympy

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

ValueError : Expected Expr or iterable but got None