65.5.2 problem 10.1 (ii)

Internal problem ID [13741]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number : 10.1 (ii)
Date solved : Tuesday, January 28, 2025 at 06:00:29 AM
CAS classification : [_linear]

\begin{align*} 1+y \,{\mathrm e}^{x}+x \,{\mathrm e}^{x} y+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve((1+exp(x)*y(x)+x*exp(x)*y(x))+(x*exp(x)+2)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.139 (sec). Leaf size: 21

DSolve[(1+Exp[x]*y[x]+x*Exp[x]*y[x])+(x*Exp[x]+2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-x+c_1}{e^x x+2} \]