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 : Tuesday, March 04, 2025 at 10:38:12 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*}

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

ode:=diff(diff(x(t),t),t) = 3*t; 
ic:=x(0) = 0, D(x)(0) = 5; 
dsolve([ode,ic],x(t), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.084 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-3*t + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 0, Subs(Derivative(x(t), t), t, 0): 5} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {t^{3}}{2} + 5 t \]