77.1.144 problem 170 (page 245)

Internal problem ID [17963]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 170 (page 245)
Date solved : Monday, March 31, 2025 at 04:52:39 PM
CAS classification : [_Lienard]

\begin{align*} y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)+2*p/x*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\operatorname {BesselY}\left (p -\frac {1}{2}, x\right ) c_2 +\operatorname {BesselJ}\left (p -\frac {1}{2}, x\right ) c_1 \right ) x^{-p +\frac {1}{2}} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 36

ode=D[y[x],{x,2}]+2*p/x*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^{\frac {1}{2}-p} \left (c_1 \operatorname {BesselJ}\left (p-\frac {1}{2},x\right )+c_2 \operatorname {BesselY}\left (p-\frac {1}{2},x\right )\right ) \]

✗ Sympy

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

TypeError : invalid input: 1 - 2*p