9.9 problem 9

Internal problem ID [12752]

Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number: 9.
ODE order: 2.
ODE degree: 1.

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

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

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

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

\[ y \left (x \right ) = \frac {c_{1} x^{3}+c_{2}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 16

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

\[ y(x)\to \frac {c_1}{x^2}+c_2 x \]