23.5.146 problem 146

Internal problem ID [6755]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 146
Date solved : Tuesday, September 30, 2025 at 03:51:25 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 42

ode:=a^4*y(x)+2*a^2*diff(diff(y(x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x) = cosh(a*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {4 a^{4} \left (c_3 x +c_1 \right ) \cos \left (a x \right )+4 a^{4} \left (c_4 x +c_2 \right ) \sin \left (a x \right )+\cosh \left (a x \right )}{4 a^{4}} \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 41

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

\begin{align*} y(x)&\to \frac {\cosh (a x)}{4 a^4}+(c_2 x+c_1) \cos (a x)+(c_4 x+c_3) \sin (a x) \end{align*}

✓ Sympy. Time used: 0.119 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- i a x} + \left (C_{3} + C_{4} x\right ) e^{i a x} + \frac {\cosh {\left (a x \right )}}{4 a^{4}} \]