7.11.41 problem 43 (b)

Internal problem ID [362]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 43 (b)
Date solved : Wednesday, February 05, 2025 at 03:24:39 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y&=\cos \left (x \right )^{3} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 43

dsolve(diff(y(x),x$4)+4*y(x)=cos(x)^3,y(x), singsol=all)
 

\[ y = \cos \left (x \right ) {\mathrm e}^{x} c_1 +c_3 \,{\mathrm e}^{-x} \cos \left (x \right )+\sin \left (x \right ) {\mathrm e}^{x} c_2 +c_4 \sin \left (x \right ) {\mathrm e}^{-x}+\frac {12 \cos \left (x \right )}{85}+\frac {\cos \left (x \right )^{3}}{85} \]

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 53

DSolve[D[y[x],{x,4}]+4*y[x]==Cos[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{340} \cos (3 x)+\left (c_1 e^{-x}+c_4 e^x+\frac {3}{20}\right ) \cos (x)+c_2 e^{-x} \sin (x)+c_3 e^x \sin (x) \]