1.17.9 problem 9

Internal problem ID [522]
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 : 9
Date solved : Tuesday, September 30, 2025 at 03:59:51 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 25

ode:=16*x^2*diff(diff(y(x),x),x)-(-144*x^3+5)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \sin \left (2 x^{{3}/{2}}\right )+c_2 \cos \left (2 x^{{3}/{2}}\right )}{x^{{1}/{4}}} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 47

ode=16*x^2*D[y[x],{x,2}]-(5-144*x^3)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{-2 i x^{3/2}} \left (6 c_1 e^{4 i x^{3/2}}+i c_2\right )}{6 \sqrt [4]{x}} \end{align*}

✓ Sympy. Time used: 0.050 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*x**2*Derivative(y(x), (x, 2)) - (5 - 144*x**3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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