Internal problem ID [1784]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.1, Singular points, Euler equations. Page 201
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 13
dsolve(t^2*diff(y(t),t$2)+5*t*diff(y(t),t)-5*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1}}{t^{5}}+c_{2} t \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[t^2*y''[t]+5*t*y'[t]-5*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_1}{t^5}+c_2 t \\ \end{align*}