7.1.14 problem 14

Internal problem ID [14]
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 : 14
Date solved : Tuesday, March 04, 2025 at 10:38:14 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=2 t +1 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=4\\ x^{\prime }\left (0\right )&=-7 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 19

ode:=diff(diff(x(t),t),t) = 2*t+1; 
ic:=x(0) = 4, D(x)(0) = -7; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = \frac {1}{3} t^{3}+\frac {1}{2} t^{2}-7 t +4 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 24

ode=D[x[t],{t,2}]==2*t+1; 
ic={x[0]==4,Derivative[1][x][0] ==-7}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {t^3}{3}+\frac {t^2}{2}-7 t+4 \]

✓ Sympy. Time used: 0.092 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-2*t + Derivative(x(t), (t, 2)) - 1,0) 
ics = {x(0): 4, Subs(Derivative(x(t), t), t, 0): -7} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {t^{3}}{3} + \frac {t^{2}}{2} - 7 t + 4 \]