Internal problem ID [11724]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 16, Higher order linear equations with constant coefficients. Exercises page
153
Problem number: 16.1 (i).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x={\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(x(t),t$3)-6*diff(x(t),t$2)+11*diff(x(t),t)-6*x(t)=exp(-t),x(t), singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{t}+{\mathrm e}^{2 t} c_{2} +c_{3} {\mathrm e}^{3 t}-\frac {{\mathrm e}^{-t}}{24} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 37
DSolve[x'''[t]-6*x''[t]+11*x'[t]-6*x[t]==Exp[-t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -\frac {e^{-t}}{24}+c_1 e^t+c_2 e^{2 t}+c_3 e^{3 t} \]