89.15.9 problem 9

Internal problem ID [24643]
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 : 9
Date solved : Thursday, October 02, 2025 at 10:46:41 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+14 y^{\prime }-8 y&=2 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=diff(diff(diff(y(x),x),x),x)-7*diff(diff(y(x),x),x)+14*diff(y(x),x)-8*y(x) = 2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {1}{4}+c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{4 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 31

ode=D[y[x],{x,3}]-7*D[y[x],{x,2}]+14*D[y[x],{x,1}]-8*y[x]==2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.118 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) + 14*Derivative(y(x), x) - 7*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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