2.10 problem 8 b(i)

Internal problem ID [12606]

Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises 1.3, page 27
Problem number: 8 b(i).
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y \left (2\right ) = 0] \end {align*}

✓ Solution by Maple

Time used: 0.11 (sec). Leaf size: 24

dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=0,y(0) = 1, y(2) = 0],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{6-x}-{\mathrm e}^{2 x}}{{\mathrm e}^{6}-1} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 29

DSolve[{y''[x]-y'[x]-2*y[x]==0,{y[0]==1,y[2]==0}},y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to \frac {e^{-x} \left (e^6-e^{3 x}\right )}{e^6-1} \]