14.13.6 problem 6

Internal problem ID [2633]
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 : 6
Date solved : Monday, January 27, 2025 at 06:04:58 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve((t-2)^2*diff(y(t),t$2)+5*(t-2)*diff(y(t),t)+4*y(t)=0,y(t), singsol=all)
 

\[ y = \frac {c_1 +c_2 \ln \left (t -2\right )}{\left (t -2\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 22

DSolve[(t-2)^2*D[y[t],{t,2}]+5*(t-2)*D[y[t],t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {2 c_2 \log (t-2)+c_1}{(t-2)^2} \]