32.7.7 problem Exercise 20.8, page 220

Internal problem ID [5922]
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 20.8, page 220
Date solved : Monday, January 27, 2025 at 01:27:34 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve(diff(y(x),x$4)-diff(y(x),x$3)-4*diff(y(x),x$2)+4*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_4 \,{\mathrm e}^{4 x}+c_3 \,{\mathrm e}^{3 x}+c_{1} {\mathrm e}^{2 x}+c_{2} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 36

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

\[ y(x)\to -\frac {1}{2} c_1 e^{-2 x}+c_2 e^x+\frac {1}{2} c_3 e^{2 x}+c_4 \]