68.14.20 problem 20

Internal problem ID [17712]
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 : 20
Date solved : Thursday, October 02, 2025 at 02:27:17 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{4 t} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 34

ode:=diff(diff(diff(y(t),t),t),t)-4*diff(diff(y(t),t),t)-11*diff(y(t),t)+30*y(t) = exp(4*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (14 c_3 \,{\mathrm e}^{8 t}-{\mathrm e}^{7 t}+14 c_2 \,{\mathrm e}^{5 t}+14 c_1 \right ) {\mathrm e}^{-3 t}}{14} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 39

ode=D[ y[t],{t,3}]-4*D[y[t],{t,2}]-11*D[y[t],t]+30*y[t]==Exp[4*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {e^{4 t}}{14}+c_1 e^{-3 t}+c_2 e^{2 t}+c_3 e^{5 t} \end{align*}

✓ Sympy. Time used: 0.136 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(30*y(t) - exp(4*t) - 11*Derivative(y(t), t) - 4*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 3 t} + C_{2} e^{2 t} + C_{3} e^{5 t} - \frac {e^{4 t}}{14} \]