63.14.2 problem 1(b)

Internal problem ID [13178]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.5 Higher order equations. Exercises page 130
Problem number : 1(b)
Date solved : Tuesday, January 28, 2025 at 05:12:01 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }+x^{\prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(diff(x(t),t$3)+diff(x(t),t)=1,x(t), singsol=all)
 

\[ x \left (t \right ) = -c_{2} \cos \left (t \right )+c_{1} \sin \left (t \right )+t +c_{3} \]

✓ Solution by Mathematica

Time used: 60.010 (sec). Leaf size: 29

DSolve[D[x[t],{t,3}]+D[x[t],t]==1,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \int _1^t(c_1 \cos (K[1])+c_2 \sin (K[1])+1)dK[1]+c_3 \]