89.14.16 problem 16

Internal problem ID [24620]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 128
Problem number : 16
Date solved : Thursday, October 02, 2025 at 10:46:32 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 8 y^{\prime \prime \prime }-4 y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=8*diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 27

ode=8*D[y[x],{x,3}]-4*D[y[x],{x,2}]-2*D[y[x],{x,1}]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.133 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 2*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + 8*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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