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 : Friday, February 07, 2025 at 08:11:54 AM
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*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

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

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

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