Internal problem ID [5874]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.4 SPECIAL
FUNCTIONS. EXERCISES 6.4. Page 267
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(2*x^2-64)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (8, \sqrt {2}\, x \right )+c_{2} \operatorname {BesselY}\left (8, \sqrt {2}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 30
DSolve[x^2*y''[x]+x*y'[x]+(2*x^2-64)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \operatorname {BesselJ}\left (8,\sqrt {2} x\right )+c_2 Y_8\left (\sqrt {2} x\right ) \\ \end{align*}