46.3.18 problem 20

Internal problem ID [9590]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.4 SPECIAL FUNCTIONS. EXERCISES 6.4. Page 267
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 06:21:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=9*x^2*diff(diff(y(x),x),x)+9*x*diff(y(x),x)+(x^6-36)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {BesselJ}\left (\frac {2}{3}, \frac {x^{3}}{9}\right )+c_2 \operatorname {BesselY}\left (\frac {2}{3}, \frac {x^{3}}{9}\right ) \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 43

ode=9*x^2*D[y[x],{x,2}]+9*x*D[y[x],x]+(x^6-36)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 c_1 \operatorname {Gamma}\left (\frac {4}{3}\right ) \operatorname {BesselJ}\left (-\frac {2}{3},\frac {x^3}{9}\right )+c_2 \operatorname {Gamma}\left (\frac {5}{3}\right ) \operatorname {BesselJ}\left (\frac {2}{3},\frac {x^3}{9}\right ) \end{align*}

✓ Sympy. Time used: 0.137 (sec). Leaf size: 22

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) + (x**6 - 36)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} J_{\frac {2}{3}}\left (\frac {x^{3}}{9}\right ) + C_{2} Y_{\frac {2}{3}}\left (\frac {x^{3}}{9}\right ) \]