73.17.12 problem 12

Internal problem ID [15467]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 12
Date solved : Thursday, March 13, 2025 at 06:04:47 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\[ y = \sqrt {x}\, \left (c_{1} \sin \left (\frac {3 \ln \left (x \right )}{2}\right )+c_{2} \cos \left (\frac {3 \ln \left (x \right )}{2}\right )\right ) \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.090 (sec). Leaf size: 27

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

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