63.5.22 problem 7

Internal problem ID [13096]
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 : Tuesday, January 28, 2025 at 04:52:10 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

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

dsolve(diff(x(t),t$2)+diff(x(t),t)=3*t,x(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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