43.10.1 problem 1(a)

Internal problem ID [8945]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 89
Problem number : 1(a)
Date solved : Tuesday, September 30, 2025 at 06:00:24 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 38

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 57

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

\begin{align*} y(x)&\to -x+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 ) \end{align*}

✓ Sympy. Time used: 0.071 (sec). Leaf size: 37

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

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