Internal problem ID [4237]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter IX, Special forms of differential equations. Examples XVII. page 247
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y}{4 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+y(x)/(4*x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, \BesselJ \left (1, \sqrt {x}\right )+c_{2} \sqrt {x}\, \BesselY \left (1, \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 38
DSolve[y''[x]+y[x]/(4*x)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \sqrt {x} \left (c_1 \text {BesselJ}\left (1,\sqrt {x}\right )+2 i c_2 Y_1\left (\sqrt {x}\right )\right ) \\ \end{align*}