37.3.11 problem 10.4.10

Internal problem ID [6417]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.4, ODEs with variable Coefficients. Second order and Homogeneous. page 318
Problem number : 10.4.10
Date solved : Thursday, March 13, 2025 at 05:58:39 PM
CAS classification : [_Laguerre]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 21

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

\[ y = c_1 \operatorname {KummerM}\left (-m , 1, x\right )+c_2 \operatorname {KummerU}\left (-m , 1, x\right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 21

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

\[ y(x)\to c_1 \operatorname {HypergeometricU}(-m,1,x)+c_2 \operatorname {LaguerreL}(m,x) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
m = symbols("m") 
y = Function("y") 
ode = Eq(m*y(x) + x*Derivative(y(x), (x, 2)) + (1 - x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False