14.13.1 problem 1

Internal problem ID [2628]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.8.1, singular points, Euler equations. Excercises page 203
Problem number : 1
Date solved : Monday, January 27, 2025 at 06:04:50 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {c_1 \,t^{6}+c_2}{t^{5}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 16

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

\[ y(t)\to \frac {c_1}{t^5}+c_2 t \]