73.12.10 problem 19.2 (d)

Internal problem ID [15283]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.2 (d)
Date solved : Thursday, March 13, 2025 at 05:51:57 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)-9*diff(diff(y(x),x),x)+31*diff(y(x),x)-39*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x} \left (c_{1} +\sin \left (2 x \right ) c_{2} +c_{3} \cos \left (2 x \right )\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 28

ode=D[y[x],{x,3}]-9*D[y[x],{x,2}]+31*D[y[x],x]-39*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.201 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-39*y(x) + 31*Derivative(y(x), x) - 9*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} \sin {\left (2 x \right )} + C_{3} \cos {\left (2 x \right )}\right ) e^{3 x} \]