1.10.29 problem 29

Internal problem ID [299]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 29
Date solved : Tuesday, September 30, 2025 at 03:54:41 AM
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);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 56

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

\begin{align*} 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 ) \end{align*}

✓ Sympy. Time used: 0.079 (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)
 

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