74.14.8 problem 8

Internal problem ID [16342]
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 : 8
Date solved : Monday, March 31, 2025 at 02:50:43 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y&=108 t \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 31

ode:=diff(diff(diff(diff(y(t),t),t),t),t)-6*diff(diff(diff(y(t),t),t),t)+13*diff(diff(y(t),t),t)-24*diff(y(t),t)+36*y(t) = 108*t; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 41

ode=D[y[t],{t,4}]-6*D[ y[t],{t,3}]+13*D[y[t],{t,2}]-24*D[y[t],t]+36*y[t]==108*t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 3 t+c_4 e^{3 t} t+c_3 e^{3 t}+c_1 \cos (2 t)+c_2 \sin (2 t)+2 \]

✓ Sympy. Time used: 0.208 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-108*t + 36*y(t) - 24*Derivative(y(t), t) + 13*Derivative(y(t), (t, 2)) - 6*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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