66.2.16 problem Problem 16

Internal problem ID [13915]
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 : Tuesday, January 28, 2025 at 06:08:25 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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