51.3.6 problem 6

Internal problem ID [10349]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 07:22:29 PM
CAS classification : [_separable]

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

Using Laplace method

✓ Maple. Time used: 0.077 (sec). Leaf size: 8

ode:=t*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t),method='laplace');
 

\[ y = c_1 \delta \left (t \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 16

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

\begin{align*} y(t)&\to \frac {c_1}{t}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.063 (sec). Leaf size: 5

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

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