68.14.10 problem 10

Internal problem ID [17702]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 10
Date solved : Thursday, October 02, 2025 at 02:27:10 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y&=153 \,{\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(y(t),t),t),t),t)-10*diff(diff(diff(y(t),t),t),t)+38*diff(diff(y(t),t),t)-64*diff(y(t),t)+40*y(t) = 153*exp(-t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_2 t +c_1 \right ) {\mathrm e}^{2 t}+\left (\sin \left (t \right ) c_4 +\cos \left (t \right ) c_3 \right ) {\mathrm e}^{3 t}+{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 48

ode=D[y[t],{t,4}]-10*D[ y[t],{t,3}]+38*D[y[t],{t,2}]-64*D[y[t],t]+40*y[t]==153*Exp[-t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-t}+c_3 e^{2 t}+c_4 e^{2 t} t+c_2 e^{3 t} \cos (t)+c_1 e^{3 t} \sin (t) \end{align*}

✓ Sympy. Time used: 0.174 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(40*y(t) - 64*Derivative(y(t), t) + 38*Derivative(y(t), (t, 2)) - 10*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 4)) - 153*exp(-t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + C_{2} t\right ) e^{2 t} + \left (C_{3} \sin {\left (t \right )} + C_{4} \cos {\left (t \right )}\right ) e^{3 t} + e^{- t} \]