6.1 problem Problem 23

Internal problem ID [2216]

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 23.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-3 y=0} \end {gather*}

Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

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

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 22

DSolve[y''[x]-2*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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