7.10.41 problem 47

Internal problem ID [311]
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 : 47
Date solved : Tuesday, March 04, 2025 at 11:07:39 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x) = (-2+2*I*3^(1/2))*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\left (1+i \sqrt {3}\right ) x}+c_2 \,{\mathrm e}^{-\left (1+i \sqrt {3}\right ) x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 41

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

\[ y(x)\to c_1 e^{x+i \sqrt {3} x}+c_2 e^{\left (-1-i \sqrt {3}\right ) x} \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 39

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

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