15.16.4 problem 4

Internal problem ID [3224]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 4
Date solved : Sunday, March 30, 2025 at 01:21:46 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+10*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \sin \left (\sqrt {6}\, \ln \left (x \right )\right )+c_2 \cos \left (\sqrt {6}\, \ln \left (x \right )\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 34

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+10*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_2 \cos \left (\sqrt {6} \log (x)\right )+c_1 \sin \left (\sqrt {6} \log (x)\right )}{x^2} \]

✓ Sympy. Time used: 0.193 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + 10*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} \sin {\left (\sqrt {6} \log {\left (x \right )} \right )} + C_{2} \cos {\left (\sqrt {6} \log {\left (x \right )} \right )}}{x^{2}} \]