7.17.5 problem 5

Internal problem ID [518]
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 : 5
Date solved : Monday, January 27, 2025 at 02:54:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 36 x^{2} y^{\prime \prime }+60 x y^{\prime }+\left (9 x^{3}-5\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(36*x^2*diff(y(x),x$2)+60*x*diff(y(x),x)+(9*x^3-5)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 44

DSolve[36*x^2*D[y[x],{x,2}]+60*x*D[y[x],x]+(9*x^3-5)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 \operatorname {AiryAi}\left (\frac {\sqrt [3]{-1} x}{2^{2/3}}\right )+c_2 \operatorname {AiryBi}\left (\frac {\sqrt [3]{-1} x}{2^{2/3}}\right )}{x^{5/6}} \]