Internal problem ID [5881]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(4*x^2*diff(y(x),x$2)+(16*x^2+1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, \BesselJ \left (0, 2 x \right )+c_{2} \sqrt {x}\, \BesselY \left (0, 2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 28
DSolve[4*x^2*y''[x]+(16*x^2+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} (c_1 J_0(2 x)+c_2 Y_0(2 x)) \\ \end{align*}