68.2.5 problem 10

Internal problem ID [17133]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 10
Date solved : Thursday, October 02, 2025 at 01:44:13 PM
CAS classification : [[_Emden, _Fowler]]

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

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

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

\[ y = x \left (x^{\sqrt {17}} c_1 +x^{-\sqrt {17}} c_2 \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to x^{1-\sqrt {17}} \left (c_2 x^{2 \sqrt {17}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \frac {C_{1}}{x^{-1 + \sqrt {17}}} + C_{2} x^{1 + \sqrt {17}} \]