34.6.16 problem 20

Internal problem ID [6090]
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
Date solved : Monday, January 27, 2025 at 01:35:35 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 31

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

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