64.10.16 problem 16

Internal problem ID [13343]
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 : 16
Date solved : Wednesday, March 05, 2025 at 09:48:32 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 37

ode:=diff(diff(diff(y(x),x),x),x)+4*diff(diff(y(x),x),x)+5*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {7}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {7}\, x}{2}\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 56

ode=D[y[x],{x,3}]+4*D[y[x],{x,2}]+5*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (c_2 e^{5 x/2} \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 e^{5 x/2} \sin \left (\frac {\sqrt {7} x}{2}\right )+c_3\right ) \]

✓ Sympy. Time used: 0.249 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) + 5*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{- 3 x} + \left (C_{1} \sin {\left (\frac {\sqrt {7} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {7} x}{2} \right )}\right ) e^{- \frac {x}{2}} \]