Internal problem ID [5240]
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).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+16 y-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 85
dsolve(diff(y(x),x$4)+16*y(x)=cos(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\cos \relax (x )}{\left (5+2 \sqrt {2}\right ) \left (-5+2 \sqrt {2}\right )}+c_{1} {\mathrm e}^{x \sqrt {2}} \cos \left (x \sqrt {2}\right )+c_{2} {\mathrm e}^{x \sqrt {2}} \sin \left (x \sqrt {2}\right )+c_{3} {\mathrm e}^{-x \sqrt {2}} \cos \left (x \sqrt {2}\right )+c_{4} {\mathrm e}^{-x \sqrt {2}} \sin \left (x \sqrt {2}\right ) \]
✓ Solution by Mathematica
Time used: 0.685 (sec). Leaf size: 74
DSolve[y''''[x]+16*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}