67.12.19 problem 19.4 (c)

Internal problem ID [16658]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.4 (c)
Date solved : Thursday, October 02, 2025 at 01:37:24 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime }-4 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-3*diff(diff(y(x),x),x)-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.043 (sec). Leaf size: 26

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

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