43.7.8 problem 4(i)

Internal problem ID [8933]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 74
Problem number : 4(i)
Date solved : Tuesday, September 30, 2025 at 06:00:17 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(diff(diff(y(x),x),x),x)-3*I*diff(diff(y(x),x),x)-3*diff(y(x),x)+I*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{i x} \left (c_3 \,x^{2}+c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 25

ode=D[y[x],{x,3}]-3*I*D[y[x],{x,2}]-3*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} (x (c_3 x+c_2)+c_1) \end{align*}

✓ Sympy. Time used: 1.060 (sec). Leaf size: 838

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

\[ \text {Solution too large to show} \]