73.17.6 problem 6

Internal problem ID [15469]
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 : 6
Date solved : Monday, March 31, 2025 at 01:38:47 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \end{align*}

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

ode:=x^2*diff(diff(y(x),x),x)-7*x*diff(y(x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{4} \left (c_1 +c_2 \ln \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 18

ode=x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^4 (4 c_2 \log (x)+c_1) \]

✓ Sympy. Time used: 0.181 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 7*x*Derivative(y(x), x) + 16*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{4} \left (C_{1} + C_{2} \log {\left (x \right )}\right ) \]