49.10.3 problem 1(c)

Internal problem ID [7661]
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(c)
Date solved : Monday, January 27, 2025 at 03:09:09 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+16 y&=\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 67

dsolve(diff(y(x),x$4)+16*y(x)=cos(x),y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right )+c_{2} {\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+c_3 \,{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right )+c_4 \,{\mathrm e}^{-\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+\frac {\cos \left (x \right )}{17} \]

✓ Solution by Mathematica

Time used: 0.673 (sec). Leaf size: 74

DSolve[D[y[x],{x,4}]+16*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\cos (x)}{17}+e^{-\sqrt {2} x} \left (\left (c_1 e^{2 \sqrt {2} x}+c_2\right ) \cos \left (\sqrt {2} x\right )+\left (c_4 e^{2 \sqrt {2} x}+c_3\right ) \sin \left (\sqrt {2} x\right )\right ) \]