13.13.1 problem Example 2

Internal problem ID [2431]
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
Date solved : Monday, January 27, 2025 at 05:52:39 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(t^2*diff(y(t),t$2)-5*t*diff(y(t),t)+9*y(t)=0,y(t), singsol=all)
 

\[ y = t^{3} \left (c_2 \ln \left (t \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 18

DSolve[t^2*D[y[t],{t,2}]-5*t*D[y[t],t]+9*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^3 (3 c_2 \log (t)+c_1) \]