Internal problem ID [5242]
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).
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 }-y-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$4)-y(x)=cos(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\cos \relax (x )}{4}-\frac {x \sin \relax (x )}{4}+c_{1} \cos \relax (x )+c_{2} {\mathrm e}^{x}+c_{3} \sin \relax (x )+c_{4} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 40
DSolve[y''''[x]-y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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) \\ \end{align*}