28.2.1 problem 1

Internal problem ID [4444]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 1
Date solved : Tuesday, March 04, 2025 at 06:44:15 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y \left (x \right ) = c_{1} {\mathrm e}^{2 x}+c_{2} \sin \left (x \right )+\cos \left (x \right ) c_3 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 24

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

\[ y(x)\to c_3 e^{2 x}+c_1 \cos (x)+c_2 \sin (x) \]

✓ Sympy. Time used: 0.128 (sec). Leaf size: 19

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

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