64.20.1 problem 1

Internal problem ID [13565]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 1
Date solved : Wednesday, March 05, 2025 at 10:03:51 PM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Maple. Time used: 8.826 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.140 (sec). Leaf size: 15

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

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