20.6.10 problem Problem 32

Internal problem ID [3705]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 32
Date solved : Monday, January 27, 2025 at 07:55:40 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 34

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

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