7.17.12 problem 12

Internal problem ID [525]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.6 (Applications of Bessel functions). Problems at page 261
Problem number : 12
Date solved : Monday, January 27, 2025 at 02:54:27 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x y^{\prime \prime }+4 x^{3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(x*diff(y(x),x$2)+4*x^3*y(x)=0,y(x), singsol=all)
 

\[ y = \left (\operatorname {BesselY}\left (\frac {1}{4}, x^{2}\right ) c_2 +\operatorname {BesselJ}\left (\frac {1}{4}, x^{2}\right ) c_1 \right ) \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 59

DSolve[D[y[x],{x,2}]+4*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt [5]{\frac {2}{5}} \sqrt {x} \left (c_1 \operatorname {Gamma}\left (\frac {4}{5}\right ) \operatorname {BesselJ}\left (-\frac {1}{5},\frac {4 x^{5/2}}{5}\right )+c_2 \operatorname {Gamma}\left (\frac {6}{5}\right ) \operatorname {BesselJ}\left (\frac {1}{5},\frac {4 x^{5/2}}{5}\right )\right ) \]