82.4.5 problem 28-5

Internal problem ID [21823]
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 : 28-5
Date solved : Thursday, October 02, 2025 at 08:02:36 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{5 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 17

ode:=diff(y(t),t)-2*y(t) = exp(5*t); 
ic:=[y(0) = 3]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \frac {8 \,{\mathrm e}^{2 t}}{3}+\frac {{\mathrm e}^{5 t}}{3} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 21

ode=D[y[t],t]-2*y[t]==Exp[5*t]; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{3} e^{2 t} \left (e^{3 t}+8\right ) \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) - exp(5*t) + Derivative(y(t), t),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (\frac {e^{3 t}}{3} + \frac {8}{3}\right ) e^{2 t} \]