1.11 problem 25

Internal problem ID [12584]

Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises page 14
Problem number: 25.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_Emden, _Fowler]]

\[ \boxed {2 x^{2} y^{\prime \prime }+y^{\prime } x -y=0} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 13

dsolve(2*x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1}}{\sqrt {x}}+c_{2} x \]

✓ Solution by Mathematica

Time used: 0.02 (sec). Leaf size: 18

DSolve[2*x^2*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to \frac {c_1}{\sqrt {x}}+c_2 x \]