89.15.8 problem 8

Internal problem ID [24642]
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 : 8
Date solved : Thursday, October 02, 2025 at 10:46:40 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&=12 \end{align*}

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

ode:=diff(diff(diff(y(x),x),x),x)+4*diff(diff(y(x),x),x) = 12; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3 x^{2}}{2}+\frac {{\mathrm e}^{-4 x} c_1}{16}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 30

ode=D[y[x],{x,3}]+4*D[y[x],{x,2}]==12; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 x^2}{2}+c_3 x+\frac {1}{16} c_1 e^{-4 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.055 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 12,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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