88.22.8 problem 12

Internal problem ID [24168]
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 160 (Laplace transform)
Problem number : 12
Date solved : Thursday, October 02, 2025 at 10:00:24 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=\cosh \left (2 x \right ) \end{align*}

Using Laplace method

✓ Maple. Time used: 0.113 (sec). Leaf size: 68

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+4*diff(diff(diff(y(x),x),x),x)+4*diff(diff(y(x),x),x) = cosh(2*x); 
dsolve(ode,y(x),method='laplace');
 

\[ y = -\frac {1}{16}+\frac {{\mathrm e}^{2 x}}{128}+x y^{\prime }\left (0\right )+y \left (0\right )+\frac {{\mathrm e}^{-2 x} \left (32 x y^{\prime \prime \prime }\left (0\right )+64 x y^{\prime \prime }\left (0\right )+8 x^{2}+32 y^{\prime \prime \prime }\left (0\right )+96 y^{\prime \prime }\left (0\right )+12 x +7\right )}{128}+\frac {y^{\prime \prime }\left (0\right ) \left (-3+4 x \right )}{4}+\frac {y^{\prime \prime \prime }\left (0\right ) \left (-1+x \right )}{4} \]

✓ Mathematica. Time used: 0.268 (sec). Leaf size: 52

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

\begin{align*} y(x)&\to \frac {1}{128} e^{-2 x} \left (e^{4 x}+4 \left (2 x^2+(4+8 c_2) x+3+8 c_1+8 c_2\right )\right )+c_4 x+c_3 \end{align*}

✗ Sympy

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

NotImplementedError : Could not solve `-cosh(2*x) + 4*Derivative(y(x), (x, 2)) + 4*Derivative(y(x),