9.2.2 problem problem 11

Internal problem ID [936]
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 11
Date solved : Tuesday, March 04, 2025 at 12:06:11 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = \left (c_4 x +c_3 \right ) {\mathrm e}^{4 x}+c_2 x +c_1 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 34

ode=D[y[x],{x,4}]-8*D[y[x],{x,3}]+16*D[y[x],{x,2}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{32} e^{4 x} (c_2 (2 x-1)+2 c_1)+c_4 x+c_3 \]

✓ Sympy. Time used: 0.078 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*Derivative(y(x), (x, 2)) - 8*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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