64.10.15 problem 15

Internal problem ID [13342]
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 : 15
Date solved : Wednesday, March 05, 2025 at 09:48:31 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+12*diff(y(x),x)-8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 23

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+12*D[y[x],x]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} (x (c_3 x+c_2)+c_1) \]

✓ Sympy. Time used: 0.167 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) + 12*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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