Internal problem ID [14752]
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: 46 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left (c_{1} \sin \left (\ln \left (x \right )\right )+c_{2} \cos \left (\ln \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 20
DSolve[x^2*y''[x]-x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (c_2 \cos (\log (x))+c_1 \sin (\log (x))) \]