48.4.24 problem 27

Internal problem ID [9894]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots Nonintegral. Exercises page 365
Problem number : 27
Date solved : Tuesday, September 30, 2025 at 06:44:05 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = x^{{1}/{3}} \left (x^{{1}/{3}} c_1 +c_2 \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \sqrt [3]{x} \left (c_2 \sqrt [3]{x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.030 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \sqrt [3]{x} \left (C_{1} + C_{2} \sqrt [3]{x}\right ) \]