52.3.9 problem 9

Internal problem ID [8295]
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 : 9
Date solved : Wednesday, March 05, 2025 at 05:34:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)+(25*x^2-4/9)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} \operatorname {BesselJ}\left (\frac {2}{3}, 5 x \right )+c_{2} \operatorname {BesselY}\left (\frac {2}{3}, 5 x \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 26

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]+(25*x^2-4/9)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}\left (\frac {2}{3},5 x\right )+c_2 \operatorname {BesselY}\left (\frac {2}{3},5 x\right ) \]

✓ Sympy. Time used: 0.242 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) + (25*x**2 - 4/9)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} J_{\frac {2}{3}}\left (5 x\right ) + C_{2} Y_{\frac {2}{3}}\left (5 x\right ) \]