68.18.28 problem 34

Internal problem ID [17872]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 34
Date solved : Thursday, October 02, 2025 at 02:29:04 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y&={\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=diff(diff(diff(y(t),t),t),t)+3*diff(diff(y(t),t),t)-9*diff(y(t),t)+5*y(t) = exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_2 \,{\mathrm e}^{-5 t}+\frac {{\mathrm e}^{t} \left (12 c_3 t +t^{2}+12 c_1 \right )}{12} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 39

ode=D[ y[t],{t,3}]+3*D[y[t],{t,2}]-9*D[y[t],t]+5*y[t]==Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t \left (\frac {t^2}{12}+\left (-\frac {1}{36}+c_3\right ) t+\frac {1}{216}+c_2\right )+c_1 e^{-5 t} \end{align*}

✓ Sympy. Time used: 0.163 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*y(t) - exp(t) - 9*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{3} e^{- 5 t} + \left (C_{1} + t \left (C_{2} + \frac {t}{12}\right )\right ) e^{t} \]