9.2.9 problem problem 18

Internal problem ID [943]
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 18
Date solved : Tuesday, March 04, 2025 at 12:06:15 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }&=16 y \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = 16*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-2 x}+c_3 \sin \left (2 x \right )+c_4 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 36

ode=D[y[x],{x,4}]==16*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{2 x}+c_3 e^{-2 x}+c_2 \cos (2 x)+c_4 \sin (2 x) \]

✓ Sympy. Time used: 0.083 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*y(x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{2 x} + C_{3} \sin {\left (2 x \right )} + C_{4} \cos {\left (2 x \right )} \]