71.2.9 problem 8 a(ii)

Internal problem ID [14341]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 8 a(ii)
Date solved : Tuesday, January 28, 2025 at 06:27:06 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 (1\right )&=3\\ y^{\prime }\left (1\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=0,y(1) = 3, D(y)(1) = -1],y(x), singsol=all)
 

\[ y = \frac {7 \,{\mathrm e}^{1-x}}{3}+\frac {2 \,{\mathrm e}^{2 x -2}}{3} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 28

DSolve[{D[y[x],{x,2}]-D[y[x],x]-2*y[x]==0,{y[1]==3,Derivative[1][y][1]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {7 e^{1-x}}{3}+\frac {2}{3} e^{2 x-2} \]