6.9 problem Problem 31

Internal problem ID [2224]

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.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 21

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

\[ y \relax (x ) = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{-4 x} \]

Solution by Mathematica

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

DSolve[y'''[x]+y''[x]-10*y'[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-4 x}+c_2 e^x+c_3 e^{2 x} \\ \end{align*}