63.15.2 problem 6(b)

Internal problem ID [13185]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 3, Laplace transform. Section 3.2.1 Initial value problems. Exercises page 156
Problem number : 6(b)
Date solved : Tuesday, January 28, 2025 at 05:12:05 AM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.121 (sec). Leaf size: 23

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

\[ x \left (t \right ) = \frac {2 \,{\mathrm e}^{-t}}{5}-\frac {2 \cos \left (2 t \right )}{5}+\frac {\sin \left (2 t \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 28

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

\[ x(t)\to e^{-t} \int _0^te^{K[1]} \sin (2 K[1])dK[1] \]