73.13.14 problem 20.1 (n)

Internal problem ID [15321]
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 (n)
Date solved : Monday, March 31, 2025 at 01:34:14 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }+37 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=4*x^2*diff(diff(y(x),x),x)+37*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 28

ode=4*x^2*D[y[x],{x,2}]+37*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.101 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) + 37*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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