52.3.10 problem 10

Internal problem ID [8296]
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 : 10
Date solved : Wednesday, March 05, 2025 at 05:34:21 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 101

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)+(2*x^2-64)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-16 c_{1} \sqrt {2}\, \left (x^{6}-75 x^{4}+1080 x^{2}-2520\right ) \operatorname {BesselJ}\left (1, \sqrt {2}\, x \right )-16 c_{2} \sqrt {2}\, \left (x^{6}-75 x^{4}+1080 x^{2}-2520\right ) \operatorname {BesselY}\left (1, \sqrt {2}\, x \right )+x \left (x^{6}-240 x^{4}+7200 x^{2}-40320\right ) \left (\operatorname {BesselJ}\left (0, \sqrt {2}\, x \right ) c_{1} +\operatorname {BesselY}\left (0, \sqrt {2}\, x \right ) c_{2} \right )}{x^{7}} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 30

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]+(2*x^2-64)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}\left (8,\sqrt {2} x\right )+c_2 \operatorname {BesselY}\left (8,\sqrt {2} x\right ) \]

✓ Sympy. Time used: 0.225 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) + (2*x**2 - 64)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} J_{8}\left (\sqrt {2} x\right ) + C_{2} Y_{8}\left (\sqrt {2} x\right ) \]