Internal problem ID [5888]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 27
dsolve(16*x^2*diff(y(x),x$2)+32*x*diff(y(x),x)+(x^4-12)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (\frac {x^{2}}{8}\right )}{x^{\frac {3}{2}}}+\frac {c_{2} \cos \left (\frac {x^{2}}{8}\right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 42
DSolve[16*x^2*y''[x]+32*x*y'[x]+(x^4-12)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {i x^2}{8}} \left (c_1-2 i c_2 e^{\frac {i x^2}{4}}\right )}{x^{3/2}} \\ \end{align*}