Internal problem ID [14122]
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: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x)=0,y(1) = 1, D(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {1+2 \ln \left (x \right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 15
DSolve[{x^2*y''[x]+5*x*y'[x]+4*y[x]==0,{y[1]==1,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 \log (x)+1}{x^2} \]