8.7.7 problem 7

Internal problem ID [813]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 7
Date solved : Monday, January 27, 2025 at 03:09:08 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: 0.006 (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: 0.009 (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]
 

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