7.1.17 problem 17

Internal problem ID [17]
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 : 17
Date solved : Friday, February 07, 2025 at 08:11:57 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=\frac {1}{\left (t +1\right )^{3}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

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

\[ x = \frac {t^{2}}{2 t +2} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 16

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

\[ x(t)\to \frac {t^2}{2 t+2} \]