7.10.39 problem 45

Internal problem ID [309]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 45
Date solved : Tuesday, March 04, 2025 at 11:07:36 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 i y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+2*I*diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{i x}+c_2 \,{\mathrm e}^{-3 i x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 26

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

\[ y(x)\to e^{-3 i x} \left (c_2 e^{4 i x}+c_1\right ) \]

✓ Sympy. Time used: 0.253 (sec). Leaf size: 42

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (\sqrt {\operatorname {complex}^{2}{\left (0,2 \right )} - 12} - \operatorname {complex}{\left (0,2 \right )}\right )}{2}} + C_{2} e^{- \frac {x \left (\sqrt {\operatorname {complex}^{2}{\left (0,2 \right )} - 12} + \operatorname {complex}{\left (0,2 \right )}\right )}{2}} \]