Internal problem ID [1495]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant
coefficient. Page 483
Problem number: section 9.2, problem 43(d).
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: 0.0 (sec). Leaf size: 59
dsolve(diff(y(x),x$6)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\left ({\mathrm e}^{\frac {x}{2}} c_{6} +{\mathrm e}^{\frac {3 x}{2}} c_{4} \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\left ({\mathrm e}^{\frac {x}{2}} c_{5} +c_{3} {\mathrm e}^{\frac {3 x}{2}}\right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{2} {\mathrm e}^{2 x}+c_{1} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 78
DSolve[y''''''[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (c_1 e^{2 x}+e^{x/2} \left (c_2 e^x+c_3\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+e^{x/2} \left (c_6 e^x+c_5\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )+c_4\right ) \]