20.6.7 problem Problem 29

Internal problem ID [3702]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 29
Date solved : Sunday, March 30, 2025 at 02:06:05 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-18*diff(y(x),x)-40*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{9 x}+c_3 \,{\mathrm e}^{3 x}+c_2 \right ) {\mathrm e}^{-5 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 30

ode=D[y[x],{x,3}]+3*D[y[x],{x,2}]-18*D[y[x],x]-40*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-5 x} \left (c_2 e^{3 x}+c_3 e^{9 x}+c_1\right ) \]

✓ Sympy. Time used: 0.179 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-40*y(x) - 18*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 5 x} + C_{2} e^{- 2 x} + C_{3} e^{4 x} \]