20.6.19 problem Problem 41

Internal problem ID [3714]
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 41
Date solved : Tuesday, March 04, 2025 at 05:08:11 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=24 \,{\mathrm e}^{-3 x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 32

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-10*diff(y(x),x)+8*y(x) = 24*exp(-3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\left (5 c_3 \,{\mathrm e}^{6 x}+5 \,{\mathrm e}^{5 x} c_{1} +6 \,{\mathrm e}^{x}+5 c_{2} \right ) {\mathrm e}^{-4 x}}{5} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 37

ode=D[y[x],{x,3}]+D[y[x],{x,2}]-10*D[y[x],x]+8*y[x]==24*Exp[-3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {6 e^{-3 x}}{5}+c_1 e^{-4 x}+c_2 e^x+c_3 e^{2 x} \]

✓ Sympy. Time used: 0.256 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*y(x) - 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 24*exp(-3*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 4 x} + C_{2} e^{x} + C_{3} e^{2 x} + \frac {6 e^{- 3 x}}{5} \]