89.12.15 problem 15

Internal problem ID [24569]
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 : 15
Date solved : Thursday, October 02, 2025 at 10:46:09 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-6 y^{\prime \prime }-28 y^{\prime }-24 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+3*diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)-28*diff(y(x),x)-24*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{5 x}+c_4 \,x^{2}+c_3 x +c_2 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 32

ode=D[y[x],{x,4}]+3*D[y[x],{x,3}]-6*D[y[x],{x,2}]-28*D[y[x],{x,1}]- 24*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (c_3 x^2+c_2 x+c_4 e^{5 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-24*y(x) - 28*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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