71.10.12 problem 17

Internal problem ID [14436]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 17
Date solved : Monday, March 31, 2025 at 12:27:08 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-(3+4*I)*diff(diff(y(x),x),x)+(-4+12*I)*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 x +c_2 \right ) {\mathrm e}^{2 i x}+c_1 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 29

ode=D[y[x],{x,3}]-(3+4*I)*D[y[x],{x,2}]-(4-12*I)*D[y[x],x]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 i x} (c_2 x+c_1)+c_3 e^{3 x} \]

✓ Sympy. Time used: 1.625 (sec). Leaf size: 1030

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(complex(-4, 12)*Derivative(y(x), x) + complex(-3, -4)*Derivative(y(x), (x, 2)) + 12*y(x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]