66.2.16 problem Problem 16

Internal problem ID [13844]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 16
Date solved : Monday, March 31, 2025 at 08:14:57 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)+(9*x^2-1/25)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {BesselJ}\left (\frac {1}{5}, 3 x \right )+c_2 \operatorname {BesselY}\left (\frac {1}{5}, 3 x \right ) \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 26

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]+(9*x^2-1/25)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}\left (\frac {1}{5},3 x\right )+c_2 \operatorname {BesselY}\left (\frac {1}{5},3 x\right ) \]

✓ Sympy. Time used: 0.215 (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) + (9*x**2 - 1/25)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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