15.16.3 problem 3

Internal problem ID [3223]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 3
Date solved : Sunday, March 30, 2025 at 01:21:44 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y&=0 \end{align*}

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

ode:=4*x^2*diff(diff(y(x),x),x)-16*x*diff(y(x),x)+25*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\ln \left (x \right ) c_2 +c_1 \right ) x^{{5}/{2}} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 25

ode=4*x^2*D[y[x],{x,2}]-16*x*D[y[x],x]+25*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} x^{5/2} (5 c_2 \log (x)+2 c_1) \]

✓ Sympy. Time used: 0.164 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) - 16*x*Derivative(y(x), x) + 25*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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