23.3.181 problem 183

Internal problem ID [5895]
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 : 183
Date solved : Tuesday, September 30, 2025 at 02:05:53 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\[ y = c_1 \operatorname {BesselI}\left (0, 2 \sqrt {x}\right )+c_2 \operatorname {BesselK}\left (0, 2 \sqrt {x}\right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 31

ode=-y[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 c_1 \operatorname {BesselI}\left (0,2 \sqrt {x}\right )+2 c_2 K_0\left (2 \sqrt {x}\right ) \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = C_{1} I_{0}\left (2 \sqrt {x}\right ) + C_{2} Y_{0}\left (2 i \sqrt {x}\right ) \]