Internal problem ID [14110]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Review exercises, page
23
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x -16 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-16*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left (x^{\sqrt {17}} c_{1} +x^{-\sqrt {17}} c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 32
DSolve[x^2*y''[x]-x*y'[x]-16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^{1-\sqrt {17}} \left (c_2 x^{2 \sqrt {17}}+c_1\right ) \]