60.3.330 problem 1347

Internal problem ID [11326]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1347
Date solved : Wednesday, March 05, 2025 at 02:20:38 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {y}{x^{4}} \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x) = -1/x*diff(y(x),x)-1/x^4*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} \operatorname {BesselJ}\left (0, \frac {1}{x}\right )+c_{2} \operatorname {BesselY}\left (0, \frac {1}{x}\right ) \]

✓ Mathematica. Time used: 0.127 (sec). Leaf size: 31

ode=D[y[x],{x,2}] == -(y[x]/x^4) - D[y[x],x]/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 \operatorname {BesselJ}\left (0,\frac {1}{x}\right )+\frac {c_1 K_0\left (\frac {i}{x}\right )}{\sqrt {\pi }} \]

✓ Sympy. Time used: 0.183 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + Derivative(y(x), x)/x + y(x)/x**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} J_{0}\left (\frac {1}{x}\right ) + C_{2} Y_{0}\left (- \frac {1}{x}\right ) \]