Internal problem ID [14712]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {2 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(2*x^2*diff(y(x),x$2)-8*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left (c_{1} x^{3}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 16
DSolve[2*x^2*y''[x]-8*x*y'[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (c_2 x^3+c_1\right ) \]