Internal problem ID [5547]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant
Coefficients. Page 62
Problem number: 5(i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -16 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-16*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x^{4}}+c_{2} x^{4} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 18
DSolve[x^2*y''[x]+x*y'[x]-16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^8+c_1}{x^4} \\ \end{align*}