Internal problem ID [5873]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.105 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(36*x^2-1/4)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (6 x \right )}{\sqrt {x}}+\frac {c_{2} \cos \left (6 x \right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 39
DSolve[x^2*y''[x]+x*y'[x]+(36*x^2-1/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-6 i x} \left (12 c_1-i c_2 e^{12 i x}\right )}{12 \sqrt {x}} \\ \end{align*}