87.22.18 problem 18

Internal problem ID [23763]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 4. The Laplace transform. Exercise at page 199
Problem number : 18
Date solved : Thursday, October 02, 2025 at 09:44:58 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-3 y&=2 \,{\mathrm e}^{t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (1\right )&={\mathrm e}^{3}-{\mathrm e} \\ \end{align*}

✓ Maple. Time used: 0.068 (sec). Leaf size: 12

ode:=diff(y(t),t)-3*y(t) = 2*exp(t); 
ic:=[y(1) = exp(3)-exp(1)]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{2 t} \sinh \left (t \right ) \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 16

ode=D[y[t],{t,1}]-3*y[t]==2*Exp[t]; 
ic={y[1]==Exp[3]-Exp[1]}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t \left (e^{2 t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 20

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

\[ y{\left (t \right )} = \left (\left (- e + 1 + e^{3}\right ) e^{2 t} - 1\right ) e^{t} \]