89.14.28 problem 28

Internal problem ID [24632]
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 128
Problem number : 28
Date solved : Thursday, October 02, 2025 at 10:46:36 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+11 y^{\prime \prime }+5 y^{\prime }-14 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 38

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-7*diff(diff(diff(y(x),x),x),x)+11*diff(diff(y(x),x),x)+5*diff(y(x),x)-14*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-x}+c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{\left (3+\sqrt {2}\right ) x}+c_4 \,{\mathrm e}^{-\left (-3+\sqrt {2}\right ) x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 51

ode=D[y[x],{x,4}]-7*D[y[x],{x,3}]+11*D[y[x],{x,2}]+5*D[y[x],{x,1}]-14*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-\left (\left (\sqrt {2}-3\right ) x\right )}+c_2 e^{\left (3+\sqrt {2}\right ) x}+c_3 e^{-x}+c_4 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-14*y(x) + 5*Derivative(y(x), x) + 11*Derivative(y(x), (x, 2)) - 7*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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