13.13.3 problem 2

Internal problem ID [2433]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.8.1, Singular points, Euler equations. Page 201
Problem number : 2
Date solved : Sunday, March 30, 2025 at 12:01:17 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {c_2 \,t^{{3}/{2}}+c_1}{t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 20

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

\[ y(t)\to \frac {c_2 t^{3/2}+c_1}{t} \]

✓ Sympy. Time used: 0.175 (sec). Leaf size: 12

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

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