15.9.13 problem 27

Internal problem ID [3070]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 27
Date solved : Sunday, March 30, 2025 at 01:17:57 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 29

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]+D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.128 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) + Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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