14.13.8 problem 8

Internal problem ID [2635]
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 : 8
Date solved : Monday, January 27, 2025 at 06:05:01 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(t^2*diff(y(t),t$2)+3*t*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
 

\[ y = \frac {c_1 \sin \left (\ln \left (t \right )\right )+c_2 \cos \left (\ln \left (t \right )\right )}{t} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 22

DSolve[t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {c_2 \cos (\log (t))+c_1 \sin (\log (t))}{t} \]