8.9.13 problem 45

Internal problem ID [857]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 45
Date solved : Tuesday, March 04, 2025 at 11:54:04 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (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);
 

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

✓ 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]
 

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

✓ Sympy. Time used: 0.262 (sec). Leaf size: 49

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)
 

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