80.8.10 problem 11

Internal problem ID [18518]
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 : Monday, March 31, 2025 at 05:41:05 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*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=diff(diff(diff(diff(x(t),t),t),t),t)-6*diff(diff(diff(x(t),t),t),t)+11*diff(diff(x(t),t),t)-6*diff(x(t),t) = exp(-3*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \,{\mathrm e}^{t}+\frac {c_2 \,{\mathrm e}^{2 t}}{2}+\frac {c_3 \,{\mathrm e}^{3 t}}{3}+\frac {{\mathrm e}^{-3 t}}{360}+c_4 \]

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

ode=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]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.277 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-6*Derivative(x(t), t) + 11*Derivative(x(t), (t, 2)) - 6*Derivative(x(t), (t, 3)) + Derivative(x(t), (t, 4)) - exp(-3*t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} + C_{2} e^{t} + C_{3} e^{2 t} + C_{4} e^{3 t} + \frac {e^{- 3 t}}{360} \]