7.17.6 problem 6

Internal problem ID [519]
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 : 6
Date solved : Monday, January 27, 2025 at 02:54:21 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} y^{\prime \prime }+24 x y^{\prime }+\left (144 x^{3}+1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

dsolve(16*x^2*diff(y(x),x$2)+24*x*diff(y(x),x)+(1+144*x^3)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_1 \operatorname {BesselJ}\left (0, 2 x^{{3}/{2}}\right )+c_2 \operatorname {BesselY}\left (0, 2 x^{{3}/{2}}\right )}{x^{{1}/{4}}} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 42

DSolve[16*x^2*D[y[x],{x,2}]+24*x*D[y[x],x]+(1+144*x^3)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 \operatorname {BesselJ}\left (0,2 x^{3/2}\right )-2 (-1)^{11/12} c_2 \operatorname {BesselY}\left (0,2 x^{3/2}\right )}{\sqrt [4]{x}} \]