7.18.5 problem 5

Internal problem ID [534]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.2 (Transformation of initial value problems). Problems at page 287
Problem number : 5
Date solved : Wednesday, February 05, 2025 at 03:42:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.232 (sec). Leaf size: 15

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

\[ x \left (t \right ) = \frac {2 \sin \left (t \right )}{3}-\frac {\sin \left (2 t \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 15

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

\[ x(t)\to -\frac {2}{3} \sin (t) (\cos (t)-1) \]