34.6.15 problem 19

Internal problem ID [6089]
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
Date solved : Monday, January 27, 2025 at 01:35:34 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }+\frac {y}{4 x}&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+y(x)/(4*x)=0,y(x), singsol=all)
 

\[ y = \left (\operatorname {BesselJ}\left (1, \sqrt {x}\right ) c_1 +\operatorname {BesselY}\left (1, \sqrt {x}\right ) c_2 \right ) \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}]+y[x]/(4*x)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \sqrt {x} \left (c_1 \operatorname {BesselJ}\left (1,\sqrt {x}\right )+2 i c_2 \operatorname {BesselY}\left (1,\sqrt {x}\right )\right ) \]