Internal problem ID [5814]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}+y x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (0, \frac {x^{2}}{2}\right )+c_{2} \operatorname {BesselY}\left (0, \frac {x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 31
DSolve[y''[x]+1/x*y'[x]+x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {BesselJ}\left (0,\frac {x^2}{2}\right )+2 c_2 \operatorname {BesselY}\left (0,\frac {x^2}{2}\right ) \]