85.60.2 problem 4

Internal problem ID [22853]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 203
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:15:46 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{-x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+11*diff(y(x),x)-6*y(x) = exp(x)+exp(-x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-x}}{24}+c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{3 x}+\frac {\left (3+4 c_1 +2 x \right ) {\mathrm e}^{x}}{4} \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 46

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==Exp[x]+Exp[-x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^{-x}}{24}+e^x \left (\frac {x}{2}+\frac {3}{4}+c_1\right )+c_2 e^{2 x}+c_3 e^{3 x} \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - exp(x) + 11*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - exp(-x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{2 x} + C_{3} e^{3 x} + \left (C_{1} + \frac {x}{2}\right ) e^{x} - \frac {e^{- x}}{24} \]