64.10.22 problem 22

Internal problem ID [13349]
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 : 22
Date solved : Wednesday, March 05, 2025 at 09:48:36 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 39

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+6*diff(diff(diff(y(x),x),x),x)+15*diff(diff(y(x),x),x)+20*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 46

ode=D[y[x],{x,4}]+6*D[y[x],{x,3}]+15*D[y[x],{x,2}]+20*D[y[x],x]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.231 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) + 20*Derivative(y(x), x) + 15*Derivative(y(x), (x, 2)) + 6*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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