23.3.33 problem 33

Internal problem ID [5747]
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 : 33
Date solved : Tuesday, September 30, 2025 at 02:02:27 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = c_1 \operatorname {AiryAi}\left (-x \right )+c_2 \operatorname {AiryBi}\left (-x \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to c_1 \operatorname {AiryAi}\left (\sqrt [3]{-1} x\right )+c_2 \operatorname {AiryBi}\left (\sqrt [3]{-1} x\right ) \end{align*}

✓ Sympy. Time used: 0.031 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} Ai\left (- x\right ) + C_{2} Bi\left (- x\right ) \]