43.4.5 problem 1(e)

Internal problem ID [8902]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 52
Problem number : 1(e)
Date solved : Tuesday, September 30, 2025 at 05:59:54 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: 26

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 38

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 \left (1+\sqrt {2}\right ) x} \left (c_2 e^{2 i \sqrt {2} x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 42

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)
 

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