81.14.20 problem 18-33

Internal problem ID [21705]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 18. Algebra of differential operators. Page 435
Problem number : 18-33
Date solved : Thursday, October 02, 2025 at 08:00:10 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=\cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 29

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

\[ y = \frac {\cos \left (2 x \right )}{15}+c_1 \cos \left (x \right )+c_2 \,{\mathrm e}^{x}+c_3 \sin \left (x \right )+c_4 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to \frac {1}{15} \cos (2 x)+c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x) \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{x} + C_{3} \sin {\left (x \right )} + C_{4} \cos {\left (x \right )} + \frac {\cos {\left (2 x \right )}}{15} \]