Internal problem ID [6193]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots
Nonintegral. Exercises page 365
Problem number: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (\ln \relax (x )\right )}{x^{2}}+\frac {c_{2} \cos \left (\ln \relax (x )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 22
DSolve[x^2*y''[x]+5*x*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \cos (\log (x))+c_1 \sin (\log (x))}{x^2} \\ \end{align*}