89.19.9 problem 9

Internal problem ID [24737]
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 : 9
Date solved : Thursday, October 02, 2025 at 10:47:33 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

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) = 16*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 41

ode=D[y[x],{x,4}]-6*D[y[x],{x,3}]+9*D[y[x],{x,2}]==16*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.064 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*exp(2*x) + 9*Derivative(y(x), (x, 2)) - 6*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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