74.18.16 problem 22

Internal problem ID [16502]
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 : 22
Date solved : Monday, March 31, 2025 at 02:54:55 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=9*diff(diff(diff(y(x),x),x),x)+36*diff(diff(y(x),x),x)+40*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 60.106 (sec). Leaf size: 43

ode=9*D[y[x],{x,3}]+36*D[y[x],{x,2}]+40*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^xe^{-2 K[1]} \left (c_2 \cos \left (\frac {2 K[1]}{3}\right )+c_1 \sin \left (\frac {2 K[1]}{3}\right )\right )dK[1]+c_3 \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(40*Derivative(y(x), x) + 36*Derivative(y(x), (x, 2)) + 9*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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