7.1.12 problem 12

Internal problem ID [12]
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 : 12
Date solved : Friday, February 07, 2025 at 08:11:50 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=-20 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=5\\ x^{\prime }\left (0\right )&=-15 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

dsolve([diff(x(t),t$2)=-20,x(0) = 5, D(x)(0) = -15],x(t), singsol=all)
 

\[ x = -10 t^{2}-15 t +5 \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 17

DSolve[{D[x[t],{t,2}]==-20,{x[0]==5,Derivative[1][x][0] ==-15}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -5 \left (2 t^2+3 t-1\right ) \]