43.10.5 problem 1(e)

Internal problem ID [8949]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 89
Problem number : 1(e)
Date solved : Tuesday, September 30, 2025 at 06:00:26 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-y(x) = cos(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: 0.02 (sec). Leaf size: 105

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

\begin{align*} y(x)&\to e^x \int _1^x\frac {1}{4} e^{-K[1]} \cos (K[1])dK[1]+e^{-x} \int _1^x-\frac {1}{4} e^{K[2]} \cos (K[2])dK[2]+\sin (x) \int _1^x-\frac {1}{2} \cos ^2(K[3])dK[3]-\frac {1}{4} \cos ^3(x)+c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x) \end{align*}

✓ Sympy. Time used: 0.076 (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)
 

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