40.8.7 problem 22

Internal problem ID [6707]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary problems. Page 86
Problem number : 22
Date solved : Sunday, March 30, 2025 at 11:20:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)+9*diff(y(x),x)-9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{x}+c_2 \sin \left (3 x \right )+c_3 \cos \left (3 x \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 26

ode=D[y[x],{x,3}]-D[y[x],{x,2}]+9*D[y[x],x]-9*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_3 e^x+c_1 \cos (3 x)+c_2 \sin (3 x) \]

✓ Sympy. Time used: 0.225 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*y(x) + 9*Derivative(y(x), x) - Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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