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 : Friday, February 07, 2025 at 08:11:53 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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