88.16.3 problem 3

Internal problem ID [24108]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 116
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:59:18 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 36

ode:=diff(diff(diff(y(x),x),x),x)-y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -1+c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 55

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

\begin{align*} y(x)&\to c_1 e^x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_3 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )-1 \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + Derivative(y(x), (x, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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