Internal problem ID [14064]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-12 y^{\prime } x +42 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(x^2*diff(y(x),x$2)-12*x*diff(y(x),x)+42*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{6} \left (c_{2} x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 16
DSolve[x^2*y''[x]-12*x*y'[x]+42*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^6 (c_2 x+c_1) \]