89.23.4 problem 4

Internal problem ID [24808]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Miscellaneous Exercises at page 162
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:48:11 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 28

ode=D[y[x],{x,3}]+D[y[x],{x,1}]==Exp[-x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^{-x}}{2}-c_2 \cos (x)+c_1 \sin (x)+c_3 \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 20

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

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