7.10.30 problem 30

Internal problem ID [300]
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 : 30
Date solved : Tuesday, March 04, 2025 at 11:07:31 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-3*diff(y(x),x)-6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 44

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

\[ y(x)\to c_3 e^{-x}+c_4 e^{2 x}+c_1 \cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \]

✓ Sympy. Time used: 0.200 (sec). Leaf size: 34

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

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