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: 0.016 (sec). Leaf size: 56
dsolve(diff(y(x),x$6)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (-\sin \left (\frac {x}{2}\right ) c_{4} +c_{6} \cos \left (\frac {x}{2}\right )\right ) {\mathrm e}^{-\frac {\sqrt {3}\, x}{2}}+\left (\sin \left (\frac {x}{2}\right ) c_{3} +\cos \left (\frac {x}{2}\right ) c_{5} \right ) {\mathrm e}^{\frac {\sqrt {3}\, x}{2}}+c_{1} \sin \left (x \right )+c_{2} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 92
DSolve[y''''''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\frac {\sqrt {3} x}{2}} \left (c_1 e^{\sqrt {3} x}+c_3\right ) \cos \left (\frac {x}{2}\right )+c_2 \cos (x)+c_4 e^{-\frac {\sqrt {3} x}{2}} \sin \left (\frac {x}{2}\right )+c_6 e^{\frac {\sqrt {3} x}{2}} \sin \left (\frac {x}{2}\right )+c_5 \sin (x) \]