75.24.4 problem 744

Internal problem ID [17216]
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 ODEs). Section 18.2. Expanding a solution in generalized power series. Bessels equation. Exercises page 177
Problem number : 744
Date solved : Tuesday, January 28, 2025 at 09:57:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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: 0.020 (sec). Leaf size: 26

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+(4*x^2-1/9)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}\left (\frac {1}{3},2 x\right )+c_2 \operatorname {BesselY}\left (\frac {1}{3},2 x\right ) \]