82.4.2 problem 28-2

Internal problem ID [21820]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 28. Laplace transforms. Page 850
Problem number : 28-2
Date solved : Thursday, October 02, 2025 at 08:02:35 PM
CAS classification : [_quadrature]

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

Using Laplace method With initial conditions

\begin{align*} y \left (\pi \right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 14

ode:=diff(y(t),t)-5*y(t) = 0; 
ic:=[y(Pi) = 2]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{5 t -5 \pi } \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

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

\begin{align*} y(t)&\to 2 e^{5 t-5 \pi } \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = \frac {2 e^{5 t}}{e^{5 \pi }} \]