1.2 problem 10.2.5

Internal problem ID [4538]

Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.2, ODEs with constant Coefficients. page 307
Problem number: 10.2.5.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_x]]

Solve \begin {gather*} \boxed {x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 17

dsolve(diff(x(t),t$3)-diff(x(t),t$2)+diff(x(t),t)-x(t)=0,x(t), singsol=all)
 

\[ x \relax (t ) = c_{1} {\mathrm e}^{t}+c_{2} \sin \relax (t )+c_{3} \cos \relax (t ) \]

Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 22

DSolve[x'''[t]-x''[t]+x'[t]-x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_3 e^t+c_1 \cos (t)+c_2 \sin (t) \\ \end{align*}