1.17.8 problem 8

Internal problem ID [521]
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 : 8
Date solved : Tuesday, September 30, 2025 at 03:59:51 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }-12 x y^{\prime }+\left (15+16 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=4*x^2*diff(diff(y(x),x),x)-12*x*diff(y(x),x)+(15+16*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 36

ode=4*x^2*D[y[x],{x,2}]-12*x*D[y[x],x]+(15+16*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 16 x^2 \left (c_1 \operatorname {BesselJ}\left (1,4 \sqrt {x}\right )+2 c_2 \operatorname {BesselY}\left (1,4 \sqrt {x}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) - 12*x*Derivative(y(x), x) + (16*x + 15)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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