20.6.18 problem Problem 40

Internal problem ID [3713]
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 40
Date solved : Sunday, March 30, 2025 at 02:06:19 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=4 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 30

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

\[ y = \frac {\left ({\mathrm e}^{4 x}+3 c_1 \,{\mathrm e}^{3 x}+3 c_3 \,{\mathrm e}^{x}+3 c_2 \right ) {\mathrm e}^{-2 x}}{3} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 37

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

\[ y(x)\to \frac {e^{2 x}}{3}+c_1 e^{-2 x}+c_2 e^{-x}+c_3 e^x \]

✓ Sympy. Time used: 0.222 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) - 4*exp(2*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)
 

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