89.11.15 problem 15

Internal problem ID [24540]
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 117
Problem number : 15
Date solved : Thursday, October 02, 2025 at 10:45:59 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 32

ode:=diff(diff(diff(y(x),x),x),x)-5*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 43

ode=D[y[x],{x,3}] -5*D[y[x],x] -2*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.118 (sec). Leaf size: 32

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

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