7.1.11 problem 11

Internal problem ID [11]
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 : 11
Date solved : Saturday, March 29, 2025 at 04:25:38 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=50 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=20\\ x^{\prime }\left (0\right )&=10 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 14

ode:=diff(diff(x(t),t),t) = 50; 
ic:=x(0) = 20, D(x)(0) = 10; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = 25 t^{2}+10 t +20 \]

✓ Mathematica. Time used: 0.067 (sec). Leaf size: 13

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

\[ x(t)\to 5 t (5 t+2) \]

✓ Sympy. Time used: 0.080 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), (t, 2)) - 50,0) 
ics = {x(0): 20, Subs(Derivative(x(t), t), t, 0): 10} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = 25 t^{2} + 10 t + 20 \]