71.2.10 problem 8 b(i)

Internal problem ID [14342]
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)
Date solved : Tuesday, January 28, 2025 at 06:27:08 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y \left (2\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.152 (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)
 

\[ y = \frac {{\mathrm e}^{-x +6}-{\mathrm e}^{2 x}}{{\mathrm e}^{6}-1} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 29

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

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