7.17.3 problem 3

Internal problem ID [516]
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 : 3
Date solved : Saturday, March 29, 2025 at 04:55:37 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x y^{\prime \prime }-y^{\prime }+36 x^{3} y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=x*diff(diff(y(x),x),x)-diff(y(x),x)+36*x^3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 24

ode=x*D[y[x],{x,2}]-D[y[x],x]+36*x^3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \cos \left (3 x^2\right )+c_2 \sin \left (3 x^2\right ) \]

✓ Sympy. Time used: 0.186 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*x**3*y(x) + x*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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