Internal problem ID [1497]
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(g).
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\relax (5)}+y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 63
dsolve(diff(y(x),x$5)+diff(y(x),x$4)+diff(y(x),x$3)+diff(y(x),x$2)+diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{4} {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{5} {\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 65
DSolve[y'''''[x]+y''''[x]+y'''[x]+y''[x]+y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (e^{x/2} \left (\left (c_3 e^x+c_2\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+\left (c_4 e^x+c_1\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )\right )+c_5\right ) \\ \end{align*}