29.5.15 problem 26

Internal problem ID [7284]
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 : 26
Date solved : Tuesday, September 30, 2025 at 04:27:47 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 89

ode:=diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-9*diff(y(x),x)-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 \,{\mathrm e}^{6 \sin \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right ) x}+c_1 \,{\mathrm e}^{2 \sqrt {3}\, \cos \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right ) x}+c_2 \,{\mathrm e}^{-2 \sqrt {3}\, \cos \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right ) x}\right ) {\mathrm e}^{\left (-2 \sin \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )-1\right ) x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 87

ode=D[y[x],{x,3}]+3*D[y[x],{x,2}]-9*D[y[x],x]-5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-9 \text {$\#$1}-5\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-9 \text {$\#$1}-5\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-9 \text {$\#$1}-5\&,1\right ]\right ) \end{align*}

✓ Sympy. Time used: 3.794 (sec). Leaf size: 1535

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) - 9*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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