62.21.3 problem Ex 3

Internal problem ID [12842]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 43. Page 92
Problem number : Ex 3
Date solved : Wednesday, March 05, 2025 at 08:48:17 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

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

\[ y = c_{1} +c_{2} {\mathrm e}^{-x}+c_3 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.084 (sec). Leaf size: 14

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

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