Internal problem ID [11502]
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).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {x^{\prime \prime \prime }+x^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(x(t),t$3)+diff(x(t),t)=1,x(t), singsol=all)
\[ x \left (t \right ) = c_{1} \sin \left (t \right )-c_{2} \cos \left (t \right )+t +c_{3} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 20
DSolve[x'''[t]+x'[t]==1,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to t-c_2 \cos (t)+c_1 \sin (t)+c_3 \]