7.17.10 problem 10

Internal problem ID [523]
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 : 10
Date solved : Monday, January 27, 2025 at 02:54:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }-2 \left (-x^{5}+14\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(2*x^2*diff(y(x),x$2)-3*x*diff(y(x),x)-2*(14-x^5)*y(x)=0,y(x), singsol=all)
 

\[ y = x^{{5}/{4}} \left (\operatorname {BesselJ}\left (\frac {\sqrt {249}}{10}, \frac {2 x^{{5}/{2}}}{5}\right ) c_1 +\operatorname {BesselY}\left (\frac {\sqrt {249}}{10}, \frac {2 x^{{5}/{2}}}{5}\right ) c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 85

DSolve[2*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]-2*(14-x^5)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^{5/4} \left (c_1 \operatorname {Gamma}\left (1-\frac {\sqrt {249}}{10}\right ) \operatorname {BesselJ}\left (-\frac {\sqrt {249}}{10},\frac {2 x^{5/2}}{5}\right )+c_2 \operatorname {Gamma}\left (1+\frac {\sqrt {249}}{10}\right ) \operatorname {BesselJ}\left (\frac {\sqrt {249}}{10},\frac {2 x^{5/2}}{5}\right )\right )}{\sqrt {5}} \]