Internal problem ID [11503]
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(c).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {x^{\prime \prime \prime }+x^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(x(t),t$3)+diff(x(t),t$2)=0,x(t), singsol=all)
\[ x \left (t \right ) = c_{1} +c_{2} t +c_{3} {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 20
DSolve[x'''[t]+x''[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to c_1 e^{-t}+c_3 t+c_2 \]