89.12.26 problem 26

Internal problem ID [24580]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 121
Problem number : 26
Date solved : Thursday, October 02, 2025 at 10:46:13 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y \left (2\right )&=0 \\ y \left (\infty \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.075 (sec). Leaf size: 14

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-diff(y(x),x)-y(x) = 0; 
ic:=[y(0) = 1, y(2) = 0, y(infinity) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 6

ode=D[y[x],{x,3}]+D[y[x],{x,2}]-D[y[x],{x,1}]-y[x] ==0; 
ic={y[0]==0,y[2] ==0,y[Infinity] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = C_{3} e^{x} + \left (C_{3} x \left (\frac {1}{2} - \frac {e^{4}}{2}\right ) - C_{3}\right ) e^{- x} \]