47.4.5 problem 53

Internal problem ID [7482]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number : 53
Date solved : Monday, January 27, 2025 at 03:01:55 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

\[ y = c_{1} \operatorname {BesselJ}\left (0, \frac {x^{2}}{2}\right )+c_{2} \operatorname {BesselY}\left (0, \frac {x^{2}}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 31

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

\[ y(x)\to c_1 \operatorname {BesselJ}\left (0,\frac {x^2}{2}\right )+2 c_2 \operatorname {BesselY}\left (0,\frac {x^2}{2}\right ) \]