43.9.7 problem 3(a)

Internal problem ID [8942]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 83
Problem number : 3(a)
Date solved : Tuesday, September 30, 2025 at 06:00:22 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-I*diff(diff(y(x),x),x)+diff(y(x),x)-I*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-i x}+{\mathrm e}^{i x} \left (c_3 x +c_2 \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 31

ode=D[y[x],{x,3}]-I*D[y[x],{x,2}]+D[y[x],x]-I*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.103 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(complex(0, -1)*y(x) + complex(0, -1)*Derivative(y(x), (x, 2)) + Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- i x} + C_{2} e^{i x} + C_{3} e^{- x \operatorname {complex}{\left (0,-1 \right )}} \]