88.17.7 problem 11

Internal problem ID [24118]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 127
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:59:23 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 39

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

\[ y = c_4 \,{\mathrm e}^{2 x}+c_1 \cos \left (x \right )+c_2 \sin \left (x \right )-\frac {{\mathrm e}^{x}}{8}+\frac {{\mathrm e}^{-x} \left (-6 \ln \left ({\mathrm e}^{x}\right )+72 c_3 -8\right )}{72} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 54

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

\begin{align*} y(x)&\to c_1 \cos (x)+\frac {1}{72} e^{-x} \left (-6 x-9 e^{2 x}+72 c_4 e^{3 x}+72 c_2 e^x \sin (x)-8+72 c_3\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE 2*y(x) + cosh(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2)