7.10.15 problem 15

Internal problem ID [285]
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 : 15
Date solved : Tuesday, March 04, 2025 at 11:07:13 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-8*diff(diff(y(x),x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=D[y[x],{x,4}]-8*D[y[x],{x,2}]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (c_3 e^{4 x}+x \left (c_4 e^{4 x}+c_2\right )+c_1\right ) \]

✓ Sympy. Time used: 0.095 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) - 8*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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