13.13.2 problem 1

Internal problem ID [2432]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.8.1, Singular points, Euler equations. Page 201
Problem number : 1
Date solved : Sunday, March 30, 2025 at 12:01:15 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

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

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

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

✓ Sympy. Time used: 0.173 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = \frac {C_{1}}{t^{5}} + C_{2} t \]