Internal problem ID [825]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.2, Higher order linear differential equations. Constant coefficients. page
180
Problem number: 11.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (6\right )}+y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 66
dsolve(diff(y(x),x$6)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (x \right )+\cos \left (x \right ) c_{2} +c_{3} {\mathrm e}^{\frac {\sqrt {3}\, x}{2}} \sin \left (\frac {x}{2}\right )-c_{4} {\mathrm e}^{-\frac {\sqrt {3}\, x}{2}} \sin \left (\frac {x}{2}\right )+c_{5} {\mathrm e}^{\frac {\sqrt {3}\, x}{2}} \cos \left (\frac {x}{2}\right )+c_{6} {\mathrm e}^{-\frac {\sqrt {3}\, x}{2}} \cos \left (\frac {x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 74
DSolve[y''''''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \cos (x)+c_5 \sin (x)+e^{-\frac {\sqrt {3} x}{2}} \left (\left (c_1 e^{\sqrt {3} x}+c_3\right ) \cos \left (\frac {x}{2}\right )+\left (c_6 e^{\sqrt {3} x}+c_4\right ) \sin \left (\frac {x}{2}\right )\right ) \\ \end{align*}