20.6.9 problem Problem 31

Internal problem ID [3704]
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 31
Date solved : Monday, January 27, 2025 at 07:55:39 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)+diff(y(x),x$2)-10*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_3 \,{\mathrm e}^{6 x}+{\mathrm e}^{5 x} c_{1} +c_{2} \right ) {\mathrm e}^{-4 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]-10*D[y[x],x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-4 x}+c_2 e^x+c_3 e^{2 x} \]