64.20.1 problem 1

Internal problem ID [13644]
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 : Tuesday, January 28, 2025 at 05:54:15 AM
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*}

✓ Solution by Maple

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

dsolve([diff(y(t),t)-y(t)=exp(3*t),y(0) = 2],y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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