7.8.7 problem 7

Internal problem ID [221]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:42:39 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 12

dsolve([diff(y(x),x$2)+diff(y(x),x)=0,y(0) = -2, D(y)(0) = 8],y(x), singsol=all)
 

\[ y = 6-8 \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 14

DSolve[{D[y[x],{x,2}]+D[y[x],x] == 0,{y[0]==-2,Derivative[1][y][0] ==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 6-8 e^{-x} \]