73.17.22 problem 22

Internal problem ID [15485]
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 : 22
Date solved : Monday, March 31, 2025 at 01:39:12 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=4*x^2*diff(diff(y(x),x),x)+8*x*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \ln \left (x \right )+c_1}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 24

ode=4*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_2 \log (x)+2 c_1}{2 \sqrt {x}} \]

✓ Sympy. Time used: 0.173 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) + 8*x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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