64.1.10 problem 4(b)

Internal problem ID [13176]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 4(b)
Date solved : Wednesday, March 05, 2025 at 09:19:52 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 27

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

\[ y(x)\to e^{-2 x} \left (e^{4 x} (c_3 x+c_2)+c_1\right ) \]

✓ Sympy. Time used: 0.220 (sec). Leaf size: 19

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

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