75.15.6 problem 437

Internal problem ID [16886]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 437
Date solved : Monday, March 31, 2025 at 03:34:44 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=0 \end{align*}

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

ode:=diff(diff(diff(y(x),x),x),x)+6*diff(diff(y(x),x),x)+11*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 27

ode=D[y[x],{x,3}]+6*D[y[x],{x,2}]+11*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (e^x \left (c_3 e^x+c_2\right )+c_1\right ) \]

✓ Sympy. Time used: 0.199 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) + 11*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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