23.3.177 problem 179

Internal problem ID [5891]
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 : 179
Date solved : Tuesday, September 30, 2025 at 02:05:51 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 39

ode=y[x] + 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 {BesselJ}\left (1,2 \sqrt {x}\right )+2 i c_2 \operatorname {BesselY}\left (1,2 \sqrt {x}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.036 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \sqrt {x} \left (C_{1} J_{1}\left (2 \sqrt {x}\right ) + C_{2} Y_{1}\left (2 \sqrt {x}\right )\right ) \]