20.6.20 problem Problem 42

Internal problem ID [3715]
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 42
Date solved : Sunday, March 30, 2025 at 02:06:21 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=6 \,{\mathrm e}^{-x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(diff(y(x),x),x),x)+5*diff(diff(y(x),x),x)+6*diff(y(x),x) = 6*exp(-x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 37

ode=D[y[x],{x,3}]+5*D[y[x],{x,2}]+6*D[y[x],x]==6*Exp[-x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -3 e^{-x}-\frac {1}{3} c_1 e^{-3 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 \]

✓ Sympy. Time used: 0.220 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 6*exp(-x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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