7.1.15 problem 15

Internal problem ID [15]
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 : 15
Date solved : Saturday, March 29, 2025 at 04:25:48 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=4 \left (t +3\right )^{2} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 16

ode:=diff(diff(x(t),t),t) = 4*(t+3)^2; 
ic:=x(0) = 1, D(x)(0) = -1; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = \frac {\left (t +3\right )^{4}}{3}-37 t -26 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 27

ode=D[x[t],{t,2}]==4*(t+3)^2; 
ic={x[0]==1,Derivative[1][x][0] ==-1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {t^4}{3}+4 t^3+18 t^2-t+1 \]

✓ Sympy. Time used: 0.106 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-4*(t + 3)**2 + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 1, Subs(Derivative(x(t), t), t, 0): -1} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {t^{4}}{3} + 4 t^{3} + 18 t^{2} - t + 1 \]