7.28 problem 53

Internal problem ID [184]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 53.
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y=0} \]

✓ 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)-12*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{2} x^{7}+c_{1}}{x^{4}} \]

✓ Solution by Mathematica

Time used: 0.01 (sec). Leaf size: 18

DSolve[x^2*y''[x]+2*x*y'[x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to \frac {c_2 x^7+c_1}{x^4} \]