Internal problem ID [5600]
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: 6.
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 }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 36
dsolve(diff(y(x),x$4)+4*diff(y(x),x$3)+6*diff(y(x),x$2)+4*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{-x} x +c_{3} {\mathrm e}^{-x} x^{2}+c_{4} {\mathrm e}^{-x} x^{3} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 28
DSolve[y''''[x]+4*y'''[x]+6*y''[x]+4*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (x (x (c_4 x+c_3)+c_2)+c_1) \\ \end{align*}