1.17.6 problem 6

Internal problem ID [519]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.6 (Applications of Bessel functions). Problems at page 261
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 03:59:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} y^{\prime \prime }+24 x y^{\prime }+\left (144 x^{3}+1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 27

ode:=16*x^2*diff(diff(y(x),x),x)+24*x*diff(y(x),x)+(144*x^3+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \operatorname {BesselJ}\left (0, 2 x^{{3}/{2}}\right )+c_2 \operatorname {BesselY}\left (0, 2 x^{{3}/{2}}\right )}{x^{{1}/{4}}} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 42

ode=16*x^2*D[y[x],{x,2}]+24*x*D[y[x],x]+(1+144*x^3)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1 \operatorname {BesselJ}\left (0,2 x^{3/2}\right )-2 (-1)^{11/12} c_2 \operatorname {BesselY}\left (0,2 x^{3/2}\right )}{\sqrt [4]{x}} \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*x**2*Derivative(y(x), (x, 2)) + 24*x*Derivative(y(x), x) + (144*x**3 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} J_{0}\left (2 x^{\frac {3}{2}}\right ) + C_{2} Y_{0}\left (2 x^{\frac {3}{2}}\right )}{\sqrt [4]{x}} \]