73.13.9 problem 20.1 (i)

Internal problem ID [15316]
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 (i)
Date solved : Monday, March 31, 2025 at 01:34:03 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

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);
 

\[ y = x^{3} \left (c_1 \sin \left (2 \sqrt {5}\, \ln \left (x \right )\right )+c_2 \cos \left (2 \sqrt {5}\, \ln \left (x \right )\right )\right ) \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 36

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]
 

\[ y(x)\to x^3 \left (c_2 \cos \left (2 \sqrt {5} \log (x)\right )+c_1 \sin \left (2 \sqrt {5} \log (x)\right )\right ) \]

✓ Sympy. Time used: 0.207 (sec). Leaf size: 32

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)
 

\[ y{\left (x \right )} = x^{3} \left (C_{1} \sin {\left (2 \sqrt {5} \log {\left (x \right )} \right )} + C_{2} \cos {\left (2 \sqrt {5} \log {\left (x \right )} \right )}\right ) \]