7.1.18 problem 18

Internal problem ID [18]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.2. Problems at page 17
Problem number : 18
Date solved : Friday, February 07, 2025 at 08:11:59 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=50 \sin \left (5 t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=8\\ x^{\prime }\left (0\right )&=-10 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 12

dsolve([diff(x(t),t$2)=50*sin(5*t),x(0) = 8, D(x)(0) = -10],x(t), singsol=all)
 

\[ x = -2 \sin \left (5 t \right )+8 \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 13

DSolve[{D[x[t],{t,2}]==50*Sin[5*t],{x[0]==8,Derivative[1][x][0] ==-10}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 8-2 \sin (5 t) \]