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 : Saturday, March 29, 2025 at 04:25:58 PM
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*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 12

ode:=diff(diff(x(t),t),t) = 50*sin(5*t); 
ic:=x(0) = 8, D(x)(0) = -10; 
dsolve([ode,ic],x(t), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.099 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-50*sin(5*t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 8, Subs(Derivative(x(t), t), t, 0): -10} 
dsolve(ode,func=x(t),ics=ics)
 

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