15.16.2 problem 2

Internal problem ID [3222]
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 : 2
Date solved : Sunday, March 30, 2025 at 01:21:42 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (4 \ln \left (x \right )\right )+c_2 \cos \left (4 \ln \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 22

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \cos (4 \log (x))+c_2 \sin (4 \log (x)) \]

✓ Sympy. Time used: 0.169 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) + 16*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (4 \log {\left (x \right )} \right )} + C_{2} \cos {\left (4 \log {\left (x \right )} \right )} \]