89.15.11 problem 11

Internal problem ID [24645]
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 : 11
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 \prime }&=11 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

\[ y = \frac {11 x^{2}}{18}+\frac {{\mathrm e}^{-9 x} c_1}{81}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 30

ode=D[y[x],{x,3}]+9*D[y[x],{x,2}]==11; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {11 x^2}{18}+c_3 x+\frac {1}{81} c_1 e^{-9 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.057 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 11,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{- 9 x} + \frac {11 x^{2}}{18} \]