63.5.22 problem 7

Internal problem ID [13017]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 7
Date solved : Wednesday, March 05, 2025 at 08:57:32 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=diff(diff(x(t),t),t)+diff(x(t),t) = 3*t; 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = -{\mathrm e}^{-t} c_{1} +\frac {3 t^{2}}{2}-3 t +c_{2} \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 27

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

\[ x(t)\to \frac {3 t^2}{2}-3 t-c_1 e^{-t}+c_2 \]

✓ Sympy. Time used: 0.141 (sec). Leaf size: 19

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

\[ x{\left (t \right )} = C_{1} + C_{2} e^{- t} + \frac {3 t^{2}}{2} - 3 t \]