Internal problem ID [15236]
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: 446.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$5)+4*diff(y(x),x$4)+5*diff(y(x),x$3)-6*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (c_{2} {\mathrm e}^{3 x}+\left (\sin \left (x \right ) c_{4} +\cos \left (x \right ) c_{5} +c_{1} \right ) {\mathrm e}^{x}+c_{3} \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 44
DSolve[y'''''[x]+4*y''''[x]+5*y'''[x]-6*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_4 e^x+c_5 e^{3 x}+c_2 e^x \cos (x)+c_1 e^x \sin (x)+c_3\right ) \]