85.54.1 problem 1

Internal problem ID [22822]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 197
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:14:59 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 41

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-y(x) = cosh(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-x} \left (-2 \ln \left ({\mathrm e}^{x}\right )+16 c_4 -3\right )}{16}+\frac {\left (16 c_2 +2 x -3\right ) {\mathrm e}^{x}}{16}+c_1 \cos \left (x \right )+c_3 \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to c_2 \cos (x)+\frac {1}{16} e^{-x} \left (-2 x+e^{2 x} (2 x-3+16 c_1)+16 c_4 e^x \sin (x)-3+16 c_3\right ) \end{align*}

✓ Sympy. Time used: 0.068 (sec). Leaf size: 19

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

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