1.20 problem 34

Internal problem ID [12593]

Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises page 14
Problem number: 34.
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y=0} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 14

dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 18

DSolve[x^2*y''[x]-5*x*y'[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to x^3 (3 c_2 \log (x)+c_1) \]