1.1.12 problem 12

Internal problem ID [12]
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 : 12
Date solved : Tuesday, September 30, 2025 at 03:38:12 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=-20 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=5 \\ x^{\prime }\left (0\right )&=-15 \\ \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 14

ode:=diff(diff(x(t),t),t) = -20; 
ic:=[x(0) = 5, D(x)(0) = -15]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -10 t^{2}-15 t +5 \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 17

ode=D[x[t],{t,2}]==-20; 
ic={x[0]==5,Derivative[1][x][0] ==-15}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -5 \left (2 t^2+3 t-1\right ) \end{align*}

✓ Sympy. Time used: 0.041 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), (t, 2)) + 20,0) 
ics = {x(0): 5, Subs(Derivative(x(t), t), t, 0): -15} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = - 10 t^{2} - 15 t + 5 \]