80.8.10 problem 11

Internal problem ID [18589]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 12:03:22 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime }&={\mathrm e}^{-3 t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

dsolve(diff(x(t),t$4)-6*diff(x(t),t$3)+11*diff(x(t),t$2)-6*diff(x(t),t)=exp(-3*t),x(t), singsol=all)
 

\[ x = \frac {\left (c_3 \,{\mathrm e}^{6 t}+3 c_{1} {\mathrm e}^{4 t}+\frac {3 \,{\mathrm e}^{5 t} c_{2}}{2}+3 c_4 \,{\mathrm e}^{3 t}+\frac {1}{120}\right ) {\mathrm e}^{-3 t}}{3} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 45

DSolve[D[x[t],{t,4}]-6*D[x[t],{t,3}]+11*D[x[t],{t,2}]-6*D[x[t],t]==Exp[-3*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {e^{-3 t}}{360}+c_1 e^t+\frac {1}{2} c_2 e^{2 t}+\frac {1}{3} c_3 e^{3 t}+c_4 \]