64.20.2 problem 2

Internal problem ID [13574]
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 : Monday, March 31, 2025 at 08:01:35 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*}

✓ Maple. Time used: 0.098 (sec). Leaf size: 11

ode:=diff(y(t),t)+y(t) = 2*sin(t); 
ic:=y(0) = -1; 
dsolve([ode,ic],y(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.130 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 2*sin(t) + Derivative(y(t), t),0) 
ics = {y(0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

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