7.1.16 problem 16

Internal problem ID [16]
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 : 16
Date solved : Friday, February 07, 2025 at 08:11:55 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=\frac {1}{\sqrt {t +4}} \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: 0.019 (sec). Leaf size: 16

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

\[ x = \frac {4 \left (t +4\right )^{{3}/{2}}}{3}-5 t -\frac {29}{3} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 23

DSolve[{D[x[t],{t,2}]==1/Sqrt[t+4],{x[0]==1,Derivative[1][x][0] ==-1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{3} \left (4 (t+4)^{3/2}-15 t-29\right ) \]