14.12.7 problem Problem 22

Internal problem ID [3801]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page 575
Problem number : Problem 22
Date solved : Tuesday, September 30, 2025 at 06:57:31 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y&=8 \,{\mathrm e}^{-x}+1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=diff(diff(diff(y(x),x),x),x)+9*diff(diff(y(x),x),x)+24*diff(y(x),x)+16*y(x) = 8*exp(-x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{16}+\frac {\left (-16+24 x +27 c_2 \right ) {\mathrm e}^{-x}}{27}+\left (c_3 x +c_1 \right ) {\mathrm e}^{-4 x} \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 39

ode=D[y[x],{x,3}]+9*D[y[x],{x,2}]+24*D[y[x],x]+16*y[x]==8*Exp[-x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-4 x} (c_2 x+c_1)+e^{-x} \left (\frac {8 x}{9}-\frac {16}{27}+c_3\right )+\frac {1}{16} \end{align*}

✓ Sympy. Time used: 0.213 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) + 24*Derivative(y(x), x) + 9*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 1 - 8*exp(-x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + \frac {8 x}{9}\right ) e^{- x} + \left (C_{2} + C_{3} x\right ) e^{- 4 x} + \frac {1}{16} \]