Internal problem ID [15229]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.2 Homogeneous differential equations with
constant coefficients. Exercises page 121
Problem number: 439.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$6)+2*diff(y(x),x$5)+diff(y(x),x$4)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{6} x +c_{5} \right ) {\mathrm e}^{-x}+c_{4} x^{3}+c_{3} x^{2}+c_{2} x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 37
DSolve[y''''''[x]+2*y'''''[x]+y''''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} (c_2 (x+4)+c_1)+x (x (c_6 x+c_5)+c_4)+c_3 \]