68.18.17 problem 23

Internal problem ID [17861]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 23
Date solved : Thursday, October 02, 2025 at 02:28:57 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=9*diff(diff(diff(y(x),x),x),x)+12*diff(diff(y(x),x),x)+13*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,{\mathrm e}^{-\frac {2 x}{3}} \sin \left (x \right )+c_3 \,{\mathrm e}^{-\frac {2 x}{3}} \cos \left (x \right ) \]

✓ Mathematica. Time used: 60.025 (sec). Leaf size: 37

ode=9*D[y[x],{x,3}]+12*D[y[x],{x,2}]+13*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^xe^{-\frac {2 K[1]}{3}} (c_2 \cos (K[1])+c_1 \sin (K[1]))dK[1]+c_3 \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(13*Derivative(y(x), x) + 12*Derivative(y(x), (x, 2)) + 9*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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