87.12.13 problem 14

Internal problem ID [23461]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 93
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:42:00 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-i y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-I*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{4 i x}+c_2 \,{\mathrm e}^{-3 i x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 26

ode=D[y[x],{x,2}]-I*D[y[x],{x,1}]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 i x} \left (c_1 e^{7 i x}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.141 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) - I*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 3 i x} + C_{2} e^{4 i x} \]