49.4.7 problem 1(g)

Internal problem ID [7618]
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(g)
Date solved : Wednesday, March 05, 2025 at 04:48:16 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)+(-1+3*I)*diff(y(x),x)-3*I*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} {\mathrm e}^{-3 i x}+{\mathrm e}^{x} c_{2} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 22

ode=D[y[x],{x,2}]+(3*I-1)*D[y[x],x]-3*I*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{-3 i x}+c_2 e^x \]

✓ Sympy. Time used: 0.306 (sec). Leaf size: 60

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (\sqrt {\operatorname {complex}^{2}{\left (-1,3 \right )} - 4 \operatorname {complex}{\left (0,-3 \right )}} - \operatorname {complex}{\left (-1,3 \right )}\right )}{2}} + C_{2} e^{- \frac {x \left (\sqrt {\operatorname {complex}^{2}{\left (-1,3 \right )} - 4 \operatorname {complex}{\left (0,-3 \right )}} + \operatorname {complex}{\left (-1,3 \right )}\right )}{2}} \]