57.3.5 problem 5

Internal problem ID [9062]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 5
Date solved : Sunday, March 30, 2025 at 02:05:59 PM
CAS classification : [_separable]

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

Using Laplace method With initial conditions

\begin{align*} y \left (x_{0} \right )&=y_{0} \end{align*}

✓ Maple. Time used: 0.120 (sec). Leaf size: 10

ode:=t*diff(y(t),t)+y(t) = 0; 
ic:=y(x__0) = y__0; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = \frac {y_{0} x_{0}}{t} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 11

ode=t*D[y[t],t]+y[t]==0; 
ic=y[x0]==y0; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {\text {x0} \text {y0}}{t} \]

✓ Sympy. Time used: 0.110 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), t) + y(t),0) 
ics = {y(x__0): y__0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {x^{0} y^{0}}{t} \]