65.9.1 problem 16.1 (i)

Internal problem ID [13780]
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)
Date solved : Tuesday, January 28, 2025 at 06:03:24 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x&={\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ x \left (t \right ) = -\frac {{\mathrm e}^{-t}}{24}+c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{3 t} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 37

DSolve[D[x[t],{t,3}]-6*D[x[t],{t,2}]+11*D[x[t],t]-6*x[t]==Exp[-t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -\frac {e^{-t}}{24}+c_1 e^t+c_2 e^{2 t}+c_3 e^{3 t} \]