35.5.11 problem 19

Internal problem ID [6145]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 19
Date solved : Sunday, March 30, 2025 at 10:41:15 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+(1+2*I)*diff(y(x),x)+(-1+I)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.271 (sec). Leaf size: 53

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

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