23.5.129 problem 129

Internal problem ID [6738]
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 : 129
Date solved : Tuesday, September 30, 2025 at 03:51:17 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 35

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = cos(x)+y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_4 \,{\mathrm e}^{-x}+\frac {\left (4 c_1 -1\right ) \cos \left (x \right )}{4}+\frac {\left (-x +4 c_3 \right ) \sin \left (x \right )}{4}+c_2 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 40

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

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

✓ Sympy. Time used: 0.086 (sec). Leaf size: 26

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

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