68.13.35 problem 59

Internal problem ID [17688]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 59
Date solved : Thursday, October 02, 2025 at 02:27:03 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+60 y^{\prime \prime }+124 y^{\prime }+75 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 32

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+12*diff(diff(diff(y(t),t),t),t)+60*diff(diff(y(t),t),t)+124*diff(y(t),t)+75*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{3 t}+c_2 \,{\mathrm e}^{t}+c_3 \sin \left (3 t \right )+c_4 \cos \left (3 t \right )\right ) {\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 40

ode=D[y[t],{t,4}]+12*D[ y[t],{t,3}]+60*D[y[t],{t,2}]+124*D[y[t],t]+75*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-4 t} \left (c_3 e^t+c_4 e^{3 t}+c_2 \cos (3 t)+c_1 \sin (3 t)\right ) \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(75*y(t) + 124*Derivative(y(t), t) + 60*Derivative(y(t), (t, 2)) + 12*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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