81.10.26 problem 14-26

Internal problem ID [21621]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 14. Second order homogeneous differential equations with constant coefficients. Page 297.
Problem number : 14-26
Date solved : Thursday, October 02, 2025 at 07:59:05 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }-3 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(y(x),x),x)-3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 41

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

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

✓ Sympy. Time used: 0.060 (sec). Leaf size: 32

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

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