89.20.10 problem 10

Internal problem ID [24766]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Oral Exercises at page 154
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:47:49 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+9 y^{\prime }&={\mathrm e}^{-3 x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 32

ode:=diff(diff(diff(y(x),x),x),x)+6*diff(diff(y(x),x),x)+9*diff(y(x),x) = exp(-3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-9 x^{2}+\left (-18 c_1 -6\right ) x -6 c_1 -18 c_2 -2\right ) {\mathrm e}^{-3 x}}{54}+c_3 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 41

ode=D[y[x],{x,3}]+6*D[y[x],{x,2}]+9*D[y[x],x]== Exp[-3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3-\frac {1}{54} e^{-3 x} \left (9 x^2+6 (1+3 c_2) x+2+18 c_1+6 c_2\right ) \end{align*}

✓ Sympy. Time used: 0.183 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - exp(-3*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \left (C_{2} + x \left (C_{3} - \frac {x}{6}\right )\right ) e^{- 3 x} \]