7.1.13 problem 13

Internal problem ID [13]
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 : 13
Date solved : Friday, February 07, 2025 at 08:11:51 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{\prime \prime }&=3 t \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 13

dsolve([diff(x(t),t$2)=3*t,x(0) = 0, D(x)(0) = 5],x(t), singsol=all)
 

\[ x = \frac {1}{2} t^{3}+5 t \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 15

DSolve[{D[x[t],{t,2}]==3*t,{x[0]==0,Derivative[1][x][0] ==5}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{2} t \left (t^2+10\right ) \]