Internal problem ID [4071]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.9, page 220.
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 }+y^{\prime \prime }-4 y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 36
dsolve(diff(y(x),x$4)+4*diff(y(x),x$3)+diff(y(x),x$2)-4*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{\left (-2+\sqrt {2}\right ) x}+c_{4} {\mathrm e}^{-\left (2+\sqrt {2}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 49
DSolve[y''''[x]+4*y'''[x]+y''[x]-4*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\left (\left (2+\sqrt {2}\right ) x\right )}+c_2 e^{\left (\sqrt {2}-2\right ) x}+c_3 e^{-x}+c_4 e^x \\ \end{align*}