32.7.8 problem Exercise 20.9, page 220

Internal problem ID [5923]
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
Date solved : Monday, January 27, 2025 at 01:27:35 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-2 y&=0 \end{align*}

✓ 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)
 

\[ y \left (x \right ) = {\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{-x}+c_3 \,{\mathrm e}^{\left (-2+\sqrt {2}\right ) x}+c_4 \,{\mathrm e}^{-\left (2+\sqrt {2}\right ) x} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 49

DSolve[D[y[x],{x,4}]+4*D[y[x],{x,3}]+D[y[x],{x,2}]-4*D[y[x],x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-\left (\left (2+\sqrt {2}\right ) x\right )}+c_2 e^{\left (\sqrt {2}-2\right ) x}+c_3 e^{-x}+c_4 e^x \]