64.10.6 problem 6

Internal problem ID [13341]
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 : 6
Date solved : Monday, March 31, 2025 at 07:51:56 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+5*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{4 x}+c_2 \,{\mathrm e}^{-x}+c_3 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 29

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+5*D[y[x],x]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} \left (e^{4 x} \left (c_3 e^x+c_2\right )+c_1\right ) \]

✓ Sympy. Time used: 0.167 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) + 5*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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