Internal problem ID [5995]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }-y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(diff(y(x),x$4)-y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{4} {\mathrm e}^{-x}+\frac {\left (4 c_{1} -1\right ) \cos \left (x \right )}{4}+\frac {\left (-x +4 c_{3} \right ) \sin \left (x \right )}{4}+{\mathrm e}^{x} c_{2} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 40
DSolve[y''''[x]-y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^x+c_3 e^{-x}+\left (-\frac {1}{2}+c_2\right ) \cos (x)+\left (-\frac {x}{4}+c_4\right ) \sin (x) \]