9.2.17 problem problem 29

Internal problem ID [951]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 29
Date solved : Tuesday, March 04, 2025 at 12:06:20 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+27 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=diff(diff(diff(y(x),x),x),x)+27*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {9 x}{2}} \sin \left (\frac {3 \sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{\frac {9 x}{2}} \cos \left (\frac {3 \sqrt {3}\, x}{2}\right )+c_1 \right ) {\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 56

ode=D[y[x],{x,3}]+27*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (c_3 e^{9 x/2} \cos \left (\frac {3 \sqrt {3} x}{2}\right )+c_2 e^{9 x/2} \sin \left (\frac {3 \sqrt {3} x}{2}\right )+c_1\right ) \]

✓ Sympy. Time used: 0.140 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(27*y(x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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