73.13.11 problem 20.1 (k)

Internal problem ID [15310]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.1 (k)
Date solved : Thursday, March 13, 2025 at 05:52:46 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y&=0 \end{align*}

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

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+29*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_{1} \sin \left (5 \ln \left (x \right )\right )+c_{2} \cos \left (5 \ln \left (x \right )\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 26

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+29*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_2 \cos (5 \log (x))+c_1 \sin (5 \log (x))}{x^2} \]

✓ Sympy. Time used: 0.196 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + 29*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} \sin {\left (5 \log {\left (x \right )} \right )} + C_{2} \cos {\left (5 \log {\left (x \right )} \right )}}{x^{2}} \]