11.2.4 problem 11

Internal problem ID [1475]
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
Date solved : Monday, January 27, 2025 at 04:57:46 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 56

dsolve(diff(y(x),x$6)+y(x)=0,y(x), singsol=all)
 

\[ y = \left (-\sin \left (\frac {x}{2}\right ) c_4 +c_6 \cos \left (\frac {x}{2}\right )\right ) {\mathrm e}^{-\frac {\sqrt {3}\, x}{2}}+\left (\sin \left (\frac {x}{2}\right ) c_3 +\cos \left (\frac {x}{2}\right ) c_5 \right ) {\mathrm e}^{\frac {\sqrt {3}\, x}{2}}+c_1 \sin \left (x \right )+c_2 \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 92

DSolve[D[y[x],{x,6}]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {\sqrt {3} x}{2}} \left (c_1 e^{\sqrt {3} x}+c_3\right ) \cos \left (\frac {x}{2}\right )+c_2 \cos (x)+c_4 e^{-\frac {\sqrt {3} x}{2}} \sin \left (\frac {x}{2}\right )+c_6 e^{\frac {\sqrt {3} x}{2}} \sin \left (\frac {x}{2}\right )+c_5 \sin (x) \]