Internal problem ID [1783]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.1, Singular points, Euler equations. Page 201
Problem number: Example 2.
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 }+9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 17
dsolve(t^2*diff(y(t),t$2)-5*t*diff(y(t),t)+9*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} t^{3}+c_{2} t^{3} \ln \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 18
DSolve[t^2*y''[t]-5*t*y'[t]+9*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t^3 (3 c_2 \log (t)+c_1) \\ \end{align*}