68.15.6 problem 6

Internal problem ID [17732]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 6
Date solved : Thursday, October 02, 2025 at 02:27:28 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 9 x^{2} y^{\prime \prime }-9 x y^{\prime }+10 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=9*x^2*diff(diff(y(x),x),x)-9*x*diff(y(x),x)+10*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 28

ode=9*x^2*D[y[x],{x,2}]-9*x*D[y[x],x]+10*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \left (c_2 \cos \left (\frac {\log (x)}{3}\right )+c_1 \sin \left (\frac {\log (x)}{3}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2*Derivative(y(x), (x, 2)) - 9*x*Derivative(y(x), x) + 10*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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