1.17.10 problem 10

Internal problem ID [523]
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 : 10
Date solved : Tuesday, September 30, 2025 at 03:59:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }-2 \left (-x^{5}+14\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

ode:=2*x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)-2*(-x^5+14)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{{5}/{4}} \left (\operatorname {BesselY}\left (\frac {\sqrt {249}}{10}, \frac {2 x^{{5}/{2}}}{5}\right ) c_2 +\operatorname {BesselJ}\left (\frac {\sqrt {249}}{10}, \frac {2 x^{{5}/{2}}}{5}\right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 85

ode=2*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]-2*(14-x^5)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^{5/4} \left (c_1 \operatorname {Gamma}\left (1-\frac {\sqrt {249}}{10}\right ) \operatorname {BesselJ}\left (-\frac {\sqrt {249}}{10},\frac {2 x^{5/2}}{5}\right )+c_2 \operatorname {Gamma}\left (1+\frac {\sqrt {249}}{10}\right ) \operatorname {BesselJ}\left (\frac {\sqrt {249}}{10},\frac {2 x^{5/2}}{5}\right )\right )}{\sqrt {5}} \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) - (28 - 2*x**5)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{\frac {5}{4}} \left (C_{1} J_{\frac {\sqrt {249}}{10}}\left (\frac {2 x^{\frac {5}{2}}}{5}\right ) + C_{2} Y_{\frac {\sqrt {249}}{10}}\left (\frac {2 x^{\frac {5}{2}}}{5}\right )\right ) \]