Internal problem ID [5541]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant
Coefficients. Page 62
Problem number: 5(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 17
dsolve(2*x^2*diff(y(x),x$2)+10*x*diff(y(x),x)+8*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[2*x^2*y''[x]+10*x*y'[x]+8*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*}