7.1.11 problem 11

Internal problem ID [11]
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 : 11
Date solved : Friday, February 07, 2025 at 08:11:47 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=50 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=20\\ x^{\prime }\left (0\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 14

dsolve([diff(x(t),t$2)=50,x(0) = 20, D(x)(0) = 10],x(t), singsol=all)
 

\[ x = 25 t^{2}+10 t +20 \]

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 13

DSolve[{D[x[t],{t,2}]==50,{x[0]==0,Derivative[1][x][0] ==10}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 5 t (5 t+2) \]