20.12.2 problem Problem 8

Internal problem ID [3796]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page 575
Problem number : Problem 8
Date solved : Sunday, March 30, 2025 at 02:08:44 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=diff(diff(diff(y(x),x),x),x)+11*diff(diff(y(x),x),x)+36*diff(y(x),x)+26*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{4 x}+c_2 \sin \left (x \right )+c_3 \cos \left (x \right )\right ) {\mathrm e}^{-5 x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 30

ode=D[y[x],{x,3}]+11*D[y[x],{x,2}]+36*D[y[x],x]+26*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-5 x} \left (c_3 e^{4 x}+c_2 \cos (x)+c_1 \sin (x)\right ) \]

✓ Sympy. Time used: 0.181 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(26*y(x) + 36*Derivative(y(x), x) + 11*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + \left (C_{2} \sin {\left (x \right )} + C_{3} \cos {\left (x \right )}\right ) e^{- 4 x}\right ) e^{- x} \]