Internal problem ID [15486]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.2. Expanding a solution in generalized power
series. Bessels equation. Exercises page 177
Problem number: 744.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-\frac {1}{9}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(4*x^2-1/9)*y(x)=0,y(x), singsol=all)
\[ y = c_{1} \operatorname {BesselJ}\left (\frac {1}{3}, 2 x \right )+c_{2} \operatorname {BesselY}\left (\frac {1}{3}, 2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 26
DSolve[x^2*y''[x]+x*y'[x]+(4*x^2-1/9)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {BesselJ}\left (\frac {1}{3},2 x\right )+c_2 \operatorname {BesselY}\left (\frac {1}{3},2 x\right ) \]