13.11 problem 11

Internal problem ID [5605]

Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number: 11.
ODE order: 4.
ODE degree: 1.

CAS Maple gives this as type [[_high_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)+2*diff(y(x),x$2)+2*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{-x} x +c_{3} \sin \relax (x )+c_{4} \cos \relax (x ) \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[y''''[x]+2*y'''[x]+2*y''[x]+2*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-x} (c_4 x+c_3)+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}