Internal problem ID [10831]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-\frac {1}{25}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (\frac {1}{5}, 3 x \right )+c_{2} \operatorname {BesselY}\left (\frac {1}{5}, 3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 26
DSolve[x^2*y''[x]+x*y'[x]+(9*x^2-1/25)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \operatorname {BesselJ}\left (\frac {1}{5},3 x\right )+c_2 Y_{\frac {1}{5}}(3 x) \\ \end{align*}