35.5.14 problem 25

Internal problem ID [6148]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 25
Date solved : Wednesday, March 05, 2025 at 12:16:46 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 23

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

\[ y = \left (c_3 \,{\mathrm e}^{5 x}+c_1 \,{\mathrm e}^{3 x}+c_2 \right ) {\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 30

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

\[ y(x)\to -\frac {1}{3} c_1 e^{-3 x}+\frac {1}{2} c_2 e^{2 x}+c_3 \]

✓ Sympy. Time used: 0.177 (sec). Leaf size: 17

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

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