89.19.10 problem 10

Internal problem ID [24738]
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. Exercises at page 151
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:47:34 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 34

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

\[ y = \frac {\left (18+27 x^{2}+6 \left (6+c_1 \right ) x +4 c_1 +6 c_2 \right ) {\mathrm e}^{-3 x}}{54}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 43

ode=D[y[x],{x,4}]+6*D[y[x],{x,3}]+9*D[y[x],{x,2}]==9*Exp[-3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{54} e^{-3 x} \left (27 x^2+6 (6+c_2) x+18+6 c_1+4 c_2\right )+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*Derivative(y(x), (x, 2)) + 6*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)) - 9*exp(-3*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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