49.10.5 problem 1(e)

Internal problem ID [7663]
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 : Monday, January 27, 2025 at 03:09:10 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

dsolve(diff(y(x),x$4)-y(x)=cos(x),y(x), singsol=all)
 

\[ y = c_4 \,{\mathrm e}^{-x}+\frac {\left (-1+4 c_{1} \right ) \cos \left (x \right )}{4}+\frac {\left (-x +4 c_3 \right ) \sin \left (x \right )}{4}+{\mathrm e}^{x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 40

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

\[ y(x)\to c_1 e^x+c_3 e^{-x}+\left (-\frac {1}{2}+c_2\right ) \cos (x)+\left (-\frac {x}{4}+c_4\right ) \sin (x) \]