Internal problem ID [5220]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 74
Problem number: 4(b).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+16 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 65
dsolve(diff(y(x),x$4)+16*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = -c_{1} {\mathrm e}^{-x \sqrt {2}} \sin \left (x \sqrt {2}\right )-c_{2} {\mathrm e}^{x \sqrt {2}} \sin \left (x \sqrt {2}\right )+c_{3} {\mathrm e}^{-x \sqrt {2}} \cos \left (x \sqrt {2}\right )+c_{4} {\mathrm e}^{x \sqrt {2}} \cos \left (x \sqrt {2}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 67
DSolve[y''''[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 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*}