Internal problem ID [2111]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 46.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-y^{\prime } x -8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.034 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x^{2}}+c_{2} x^{4} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[x^2*y''[x]-x*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^6+c_1}{x^2} \\ \end{align*}