7.17.11 problem 11

Internal problem ID [524]
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 : 11
Date solved : Monday, January 27, 2025 at 02:54:25 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

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

\[ y = \left (\operatorname {BesselY}\left (\frac {1}{6}, \frac {x^{3}}{3}\right ) c_2 +\operatorname {BesselJ}\left (\frac {1}{6}, \frac {x^{3}}{3}\right ) c_1 \right ) \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 53

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

\[ y(x)\to \frac {\sqrt {x} \left (c_1 \operatorname {Gamma}\left (\frac {5}{6}\right ) \operatorname {BesselJ}\left (-\frac {1}{6},\frac {x^3}{3}\right )+c_2 \operatorname {Gamma}\left (\frac {7}{6}\right ) \operatorname {BesselJ}\left (\frac {1}{6},\frac {x^3}{3}\right )\right )}{\sqrt [6]{6}} \]