82.4.3 problem 28-3

Internal problem ID [21821]
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 : 28-3
Date solved : Thursday, October 02, 2025 at 08:02:35 PM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 10

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

\[ y = {\mathrm e}^{5 t} t \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 12

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

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 8

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

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