64.10.21 problem 21

Internal problem ID [13348]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 21
Date solved : Wednesday, March 05, 2025 at 09:48:35 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-3*diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)+2*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x} c_{1} +{\mathrm e}^{2 x} c_{2} +c_{3} \sin \left (x \right ) {\mathrm e}^{-x}+c_4 \,{\mathrm e}^{-x} \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 37

ode=D[y[x],{x,4}]-3*D[y[x],{x,3}]-2*D[y[x],{x,2}]+2*D[y[x],x]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.234 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) + 2*Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) - 3*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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