85.28.5 problem 5

Internal problem ID [22612]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 60
Problem number : 5
Date solved : Thursday, October 02, 2025 at 08:55:02 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (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: 0.023 (sec). Leaf size: 23

ode=D[y[x],{x,3}]-D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^x-c_2 e^{-x}+c_3 \end{align*}

✓ Sympy. Time used: 0.039 (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)
 

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