Internal problem ID [15235]
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: 445.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)+4*diff(y(x),x$2)-2*diff(y(x),x)-5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{3} \sin \left (2 x \right )+c_{4} \cos \left (2 x \right )+c_{1} \right ) {\mathrm e}^{-x}+c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 36
DSolve[y''''[x]+2*y'''[x]+4*y''[x]-2*y'[x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (c_4 e^{2 x}+c_2 \cos (2 x)+c_1 \sin (2 x)+c_3\right ) \]