Internal problem ID [5061]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}+y x^{2}=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = c_{1} \BesselJ \left (0, \frac {x^{2}}{2}\right )+c_{2} \BesselY \left (0, \frac {x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 31
DSolve[y''[x]+1/x*y'[x]+x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 J_0\left (\frac {x^2}{2}\right )+2 c_2 Y_0\left (\frac {x^2}{2}\right ) \\ \end{align*}