Internal problem ID [13791]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Review exercises, page
23
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \sin \left (\ln \left (x \right )\right )}{x}+\frac {c_{2} \cos \left (\ln \left (x \right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 22
DSolve[x^2*y''[x]+3*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \cos (\log (x))+c_1 \sin (\log (x))}{x} \]