89.12.29 problem 29

Internal problem ID [24583]
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 : 29
Date solved : Thursday, October 02, 2025 at 10:46:14 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+3 y^{\prime }-9 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.074 (sec). Leaf size: 12

ode:=diff(diff(diff(y(x),x),x),x)+5*diff(diff(y(x),x),x)+3*diff(y(x),x)-9*y(x) = 0; 
ic:=[y(0) = -1, y(1) = 0, y(infinity) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 14

ode=D[y[x],{x,3}]+5*D[y[x],{x,2}]+3*D[y[x],{x,1}]-9*y[x] ==0; 
ic={y[0]==-1,y[1]==0,y[Infinity]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} (x-1) \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*y(x) + 3*Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): -1, y(1): 0, y(oo): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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