7.10.36 problem 36

Internal problem ID [306]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 36
Date solved : Tuesday, March 04, 2025 at 11:07:34 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{-x} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 24

ode:=9*diff(diff(diff(y(x),x),x),x)+11*diff(diff(y(x),x),x)+4*diff(y(x),x)-14*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{\frac {16 x}{9}}+c_2 \sin \left (x \right )+\cos \left (x \right ) c_3 \right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 32

ode=9*D[y[x],{x,3}]+11*D[y[x],{x,2}]+4*D[y[x],x]-14*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} \left (c_3 e^{16 x/9}+c_2 \cos (x)+c_1 \sin (x)\right ) \]

✓ Sympy. Time used: 0.210 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-14*y(x) + 4*Derivative(y(x), x) + 11*Derivative(y(x), (x, 2)) + 9*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{\frac {7 x}{9}} + \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{- x} \]