Internal problem ID [4238]
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: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(x*diff(y(x),x$2)+diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \BesselJ \left (0, 2 \sqrt {x}\right )+c_{2} \BesselY \left (0, 2 \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 27
DSolve[x*y''[x]+y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \, _0\tilde {F}_1(;1;-x)+2 c_2 Y_0\left (2 \sqrt {x}\right ) \\ \end{align*}