3.2.6 problem problem 15

Internal problem ID [940]
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 15
Date solved : Tuesday, September 30, 2025 at 04:19:51 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 54

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-16*diff(diff(y(x),x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{2 \sqrt {2}\, \left (1+\sqrt {3}\right ) x}+c_3 \,{\mathrm e}^{2 \sqrt {2}\, x}+c_4 \,{\mathrm e}^{2 \sqrt {2}\, x \sqrt {3}}+c_1 \right ) {\mathrm e}^{-\sqrt {2}\, \left (1+\sqrt {3}\right ) x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 86

ode=D[y[x],{x,4}]-16*D[y[x],{x,2}]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{2 \sqrt {2-\sqrt {3}} x}+c_2 e^{-2 \sqrt {2-\sqrt {3}} x}+c_3 e^{2 \sqrt {2+\sqrt {3}} x}+c_4 e^{-2 \sqrt {2+\sqrt {3}} x} \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 70

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) - 16*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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