89.15.6 problem 6

Internal problem ID [24640]
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 : 6
Date solved : Thursday, October 02, 2025 at 10:46:40 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+4 y&=14 \end{align*}

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

ode:=diff(diff(diff(y(x),x),x),x)-5*diff(diff(y(x),x),x)+4*y(x) = 14; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {7}{2}+c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{2 \left (1+\sqrt {2}\right ) x}+c_3 \,{\mathrm e}^{-2 \left (\sqrt {2}-1\right ) x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 45

ode=D[y[x],{x,3}]-5*D[y[x],{x,2}]+4*y[x]==14; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-2 \left (\sqrt {2}-1\right ) x}+c_2 e^{2 \left (1+\sqrt {2}\right ) x}+c_3 e^x+\frac {7}{2} \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 14,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{x} + \left (C_{1} e^{- 2 \sqrt {2} x} + C_{2} e^{2 \sqrt {2} x}\right ) e^{2 x} + \frac {7}{2} \]