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]]
\[ \boxed {y^{\left (5\right )}+y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
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)
\[ y \left (x \right ) = {\mathrm e}^{-x} \left (\left ({\mathrm e}^{\frac {x}{2}} c_{5} +c_{3} {\mathrm e}^{\frac {3 x}{2}}\right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\left (c_{2} {\mathrm e}^{\frac {3 x}{2}}+c_{4} {\mathrm e}^{\frac {x}{2}}\right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 70
DSolve[y'''''[x]+y''''[x]+y'''[x]+y''[x]+y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (e^{x/2} \left (c_3 e^x+c_2\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+e^{x/2} \left (c_4 e^x+c_1\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )+c_5\right ) \]