43.9.8 problem 3(b)

Internal problem ID [8943]
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(b)
Date solved : Tuesday, September 30, 2025 at 06:00:23 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 i y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)-2*I*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to e^{i x} (c_2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 49

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (\sqrt {\operatorname {complex}^{2}{\left (0,-2 \right )} + 4} - \operatorname {complex}{\left (0,-2 \right )}\right )}{2}} + C_{2} e^{- \frac {x \left (\sqrt {\operatorname {complex}^{2}{\left (0,-2 \right )} + 4} + \operatorname {complex}{\left (0,-2 \right )}\right )}{2}} \]