76.1.15 problem 15

Internal problem ID [17314]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 09:59:41 AM
CAS classification : [_separable]

\begin{align*} x +y \,{\mathrm e}^{-x} y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.159 (sec). Leaf size: 17

dsolve([x+y(x)*exp(-x)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.777 (sec). Leaf size: 19

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

\[ y(x)\to \sqrt {-2 e^x (x-1)-1} \]