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 : Sunday, March 30, 2025 at 12:12:06 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*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.238 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t - 2)**2*Derivative(y(t), (t, 2)) + (5*t - 10)*Derivative(y(t), t) + 4*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{\left (t - 2\right )^{2}} \]