89.15.10 problem 10

Internal problem ID [24644]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 9. Nonhomogeneous Equations: Undetermined coefficients. Oral Exercises at page 131
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:46:41 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=11 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)+9*diff(y(x),x) = 11; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sin \left (3 x \right ) c_1}{3}-\frac {\cos \left (3 x \right ) c_2}{3}+\frac {11 x}{9}+c_3 \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 33

ode=D[y[x],{x,3}]+9*D[y[x],{x,1}]==11; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{9} (11 x-3 c_2 \cos (3 x)+3 c_1 \sin (3 x)+9 c_3) \end{align*}

✓ Sympy. Time used: 0.094 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*Derivative(y(x), x) + Derivative(y(x), (x, 3)) - 11,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \sin {\left (3 x \right )} + C_{3} \cos {\left (3 x \right )} + \frac {11 x}{9} \]