12.18.14 problem section 9.2, problem 14

Internal problem ID [2128]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 14
Date solved : Saturday, March 29, 2025 at 11:49:09 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x)+7*diff(diff(y(x),x),x)-6*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 26

ode=D[y[x],{x,4}]-4*D[y[x],{x,3}]+7*D[y[x],{x,2}]-6*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.170 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 6*Derivative(y(x), x) + 7*Derivative(y(x), (x, 2)) - 4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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