51.3.7 problem 7

Internal problem ID [10350]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 7
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 With initial conditions

\begin{align*} y \left (1\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.120 (sec). Leaf size: 9

ode:=t*diff(y(t),t)+y(t) = 0; 
ic:=[y(1) = 5]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \frac {5}{t} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 10

ode=t*D[y[t],t]+y[t]==0; 
ic=y[1]==5; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {5}{t} \end{align*}

✓ Sympy. Time used: 0.065 (sec). Leaf size: 5

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), t) + y(t),0) 
ics = {y(1): 5} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {5}{t} \]