71.2.8 problem 8 a(i)

Internal problem ID [14340]
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(i)
Date solved : Tuesday, January 28, 2025 at 06:27:04 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 )&=2\\ y^{\prime }\left (0\right )&=-5 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=0,y(0) = 2, D(y)(0) = -5],y(x), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{-x}-{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 19

DSolve[{D[y[x],{x,2}]-D[y[x],x]-2*y[x]==0,{y[0]==2,Derivative[1][y][0] ==-5}},y[x],x,IncludeSingularSolutions -> True]
 

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