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 : Tuesday, March 04, 2025 at 02:32:39 PM
CAS classification : [[_Emden, _Fowler]]

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

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

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

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

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

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

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

✓ Sympy. Time used: 0.206 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) + 3*t*Derivative(y(t), t) + 2*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1} \sin {\left (\log {\left (t \right )} \right )} + C_{2} \cos {\left (\log {\left (t \right )} \right )}}{t} \]