64.20.2 problem 2

Internal problem ID [13645]
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 : 2
Date solved : Tuesday, January 28, 2025 at 05:54:16 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=2 \sin \left (t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 8.396 (sec). Leaf size: 11

dsolve([diff(y(t),t)+y(t)=2*sin(t),y(0) = -1],y(t), singsol=all)
 

\[ y = -\cos \left (t \right )+\sin \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 29

DSolve[{D[y[t],t]+y[t]==2*Sin[t],{y[0]==-1}},{y[t]},t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (\int _0^t2 e^{K[1]} \sin (K[1])dK[1]-1\right ) \]