Internal problem ID [2096]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x^{2}}+\frac {c_{2} \ln \relax (x )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[x^2*y''[x]+5*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 c_2 \log (x)+c_1}{x^2} \\ \end{align*}