15.10.12 problem 12

Internal problem ID [3099]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 12
Date solved : Tuesday, March 04, 2025 at 03:58:36 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-8 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

ode:=diff(diff(diff(y(x),x),x),x)-8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} {\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right )+c_3 \,{\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 42

ode=D[y[x],{x,3}]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.104 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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